1F: Locate three events with Chen, one at a time. On the third meeting, fight and defeat her
Chen is a required party member to complete the main game
Easily one of the most fragile characters in the game, thanks to terrible HP, DEF, MND, affinities, and ailment resistances. In an early, unpatched version of the game, her EVA would have allowed her some survivability, but as it's busted in current versions, you ultimately can't depend on her to survive anything. However, Chen just plain shouldn't be on the field when something dangerous comes her way. Chen's role is to make use of her incredible speed and moderate attack growth - made better by her ridiculously fast leveling - to deal out a huge total of damage and then retreat. Kimontonkou followed by repeated Flight of Idaten allows Chen to get in a large number of attacks on a boss, especially if it's following a large-delay attack on a paralyzed or slowed foe; in early stretches of the game Chen's SP will run out before the boss can act, so swap her back out at that point for someone else. When using her in random encounters, Chen can outspeed even the fastest enemies, and although she packs a surprisingly strong spell card for such encounters (Phoenix Spread Wings, which factors in so little of the target's DEF stat), it is still a row-target spell card, thus reducing damage to multi-enemy parties. Be aware that she most likely won't pack the punch to take out everything by herself. Otherwise, compared to Aya (who boasts 1 extra SPD in growth rate), Chen will likely maintain the highest SPD in the game due to her fast leveling. This combined with her decent ATK and incredible attacking rate, Chen should not be underestimated even later in the game offensively.
1F: Find at least one event in which you hear someone crying. Then, find and defeat Meiling
One of the most reliable and steadfast tanks in the game, Meiling excels at her job by not excelling in any singular area, but rather by being above-average in several defensive stats, especially HP and DEF. Very few physical attacks will outright be able to run Meiling through, and you can depend on her to survive attacks that will tear apart the rest of your party in a pinch, especially if given defensive buffs. While she's sitting out on the front lines, she provides some essential support too - Colorful Rain allows her to take care of her own HP fairly well, and Healer is great for patching up low-HP characters, plus its status healing is the first move of its kind in the game. Keep in mind that Colorful Rain's power is mostly boosted by her ATK, so if she is given enough ATK and ATK buffs then not only will it heal more, but Mountain Breaker's damage output will start rising to reliable, steady numbers. While her attacks will initially start falling short of others' attacks (limiting her usefulness in regular encounters), Meiling will continue to be not only an extremely valuable and reliable tank for your party in boss fights (especially if given gear to aid her status resistances as the game progresses) but also a reliable (yet not extremely damaging) attacker with Mountain Breaker's low target DEF influence and non-elemental nature.
2F: Find Cirno four times. On the fourth, defeat Cirno
Cirno is a required party member to complete the game
Similar to Chen, Cirno is very fast, and very fragile too. Yet, she brings with her some very valuable capabilities. Because of her high speed, you can often count on her to strike before all but the fastest enemies, giving you the chance to take advantage of Cirno's main use - disabling them before they can counterattack. The Speed debuffs inflicted by Cirno's spells, especially Icicle Fall, are the strongest you'll ever have available, and they are great for quickly debilitating a boss and granting yourself more time for setting up buffs and beginning your assault. Obviously this doesn't work on everything, but Cirno's reliable PAR effect on Diamond Blizzard also shouldn't be ignored, especially in random battles, as there's a surprising number of enemies who don't resist it, thus neutering many dangerous enemies before battle even begins. Unfortunately, as the game progresses, Cirno's below-average damage capabilities don't help her out, especially with more characters appearing that can reduce enemy stats and inflict PAR as well, and many bosses gaining higher debuff resistance overall. Though, don't understimate her - even in those situations, if her speed debuff only lands once, that's all you need to make a big difference.
2F: Recruit Cirno and Meiling, then return to the frozen Minoriko
1F: Take frozen Minoriko to the sunny area to be defrosted
A nearly-dedicated cleric, Minoriko is the first character you'll get with strong, single-target healing, and may very well be the best at it. Despite her fairly low stat growths, she levels fast to compensate for that to some degree. This won't fix the fact that she tends to be easily taken down should the enemy choose to use the wrong (right?) attack against her, but as she can buff up anyone's defenses - even her own - it is mitigated to a small degree, plus her MAG is generally sufficient enough that she can focus her bonuses more into her defenses. More importantly, thanks to her good MAG and SPD combined with the high multiplier, nearly-free cost, and low delay on Promise of the Wheat God, she's able to throw around effective healing spells with ease and really help your party out, even when she first joins. Just be aware that she might not be able to keep up with the damage output from faster, multi-targetting bosses, but bosses limited to one target will have a hard time outpacing Minoriko's healing. While her attack spells don't pack much of a punch despite their defense-piercing formulas, Minoriko's simple and quick healing and defensive buff are reliable, and so long as you can deal with her relative frailty, you'll find a great healer.
2F: Recruit Cirno. You will be able to cross a gap to a new area, meet and defeat Youmu
Youmu is a mandatory party member as she guards the stairs to 3F
Youmu's a real physical powerhouse, the first of her kind, but never the same as any others you'll recruit later. Early in the game, Youmu can sweep aside enemy groups with ease; however, her SP restricts her from attacking much before she needs to be swapped into the back. Youmu's terrible SP growth also results in this being a problem that will never really go away, either - the farther you get, the more you'll need her strong attacks, and it will still be costly for you to use her. With that said, however, Youmu becomes more and more capable as the game goes on. Her damage output is excellent, and she has some good survivability so long as she's not hit by magic. This allows her to sit out on the field and use her speciality - focusing. Focus restores double the normal amount of SP for her. Due to the way it's calculated, this means that every +1 Recovery granted to her by equipment becomes +4 SP recovered on focusing. Later in the game, as equipment which boosts both ATK and Recovery becomes available, Youmu's values will really begin to kick in, and her SP issues will be far more bearable when she's become a powerful nuke.
4F (West & East): Search for and defeat three of Alice's dolls, and the Ifrit
3F: Use the newly opened teleporter to reach a new area, and defeat the fourth doll
4F (Via staircase at start of 3F): Use the new teleporter, and defeat Alice
Alice and her quest are mandatory as she guards the stairs to 5F
A mage with some unusual qualities, Alice is quite versatile. For starters, despite being a mage, she's got decent DEF and HP to survive where other attacking mages would fall, on top of the usual high MND. She's got decent speed too, and even early SP won't be much of an issue for her. Her downside is the generally lower damage output she'll be doing when compared with other dedicated magic attackers, but you won't mind, because Alice brings some tactical advantages to the table to make up for it. The first is that she's capable of attacking a target's DEF or MND, meaning that an enemy resistant to one of her attacks will usually have a vulnerability to another - as both of these still use her MAG stat, this puts her at a unique advantage. The second is the minor debuffs which her attacks inflict. These are a side effect, but in the early game she's your first access to many of these, and even later on they are a nice touch when they work. Thirdly, note that Seeker Dolls and Little Legion are non-elemental and deal reliable damage, so you will only have to worry about enemy DEF and MND (not elemental resistances) when Alice attacks with those spell cards. As a side note, Return Inanimateness deals a great amount of damage compared to her other spells and serves as a MAG version of Yuugi's Knockout in Three Steps all the way through mid-game (especially since both spell cards target enemy DEF), with generally less damage output and much better delay. Essentially, Alice isn't a master in any department, but her versatility and reliability will be a great boon to many teams.
An odd case of working both better and worse than expected, Rumia is a character you'll need to try out yourself to really grasp if she'll work for you or not. Although her stats leave a great deal to be desired, she levels fast to offset those to a degree, although she'll never have great defenses in any one area. Instead, Rumia brings some cheap and unusual spells with her. Moonlight Ray is a cheap and startlingly powerful MYS elemental spell. Demarcation, while initially healing for only negligible HP and being a situational spell, becomes a decent maintenance spell if Rumia is backed by any of the later members that are capable of boosting her MAG. Finally, while Dark Side of the Moon is your first completely defense-ignoring spell, it has very low damage output between its low formula and Rumia's low MAG, and while generally useless, can prove highly useful against a select few enemies.
The character whose strength is hardest to measure accurately, Wriggle almost exclusively relies on poisoning foes for damage output. Since poison damage isn't visible, it can be very difficult to see just how much damage she's actually doing during a battle, but if used her damage is potentially enough to drop most boss' HP significantly. Her poison effects are far stronger than that of any other character in the game and are boosted by her fast leveling rate, so even if she just lays out a single Comet on Earth and then retreats for a while, she will produce damage comparable to many strong nukes. However, since this takes time and her natural attack power is very low, she is far more capable against bosses than random encounters. While poison damage can be quite potent in the main game, during the post-game both enemies and allies alike will boast enormous speed, giving Wriggle's poison much less time to work and vastly reducing her damage output. It's worth noting that, as her main function is inflicting the poison ailment upon bosses (whose damage is purely level-based), if you want to really make the most of her, you can actually turn her into a decent secondary tank, as her ailment resistances are among the best in the game. She can also function as a good switcher by buffing her fairly respectable HP and defenses with no loss to the poison's effectiveness and no need to have her repeatedly fire off spells. Even if you put all your focus into increasing Wriggle's survivability, however, Butterfly Storm is still powerful enough to be useful in softening up or finishing off random encounters at least through the mid-game.
5F: Once you've encountered over 400 Battles, examine the spring in the northwest corner to fight Yuugi
Big, slow and packing overwhelming strength, Yuugi bears the distinction of having the second highest ATK growth rate in the game, and she puts it to extremely good use. While it takes her a bit to get moving, and her SP growth is slow enough that she can usually only get off a couple of attacks before needing a rest, Yuugi rarely needs more than those couple of attacks to lay out anything in her path. She excels at dealing damage to single targets - despite its incredible delay and her low speed, Knockout in Three Steps is a contender for one of the game's most powerful attacks, and her awesome ATK only makes that even better, utterly obliterating anything not resistant to FIR. Even if Knockout is resisted, Yuugi can still deal reliably high damage with the non-elemental spell card Supernatural Phenomenon. Irremovable Shackles is a nice option if you need status in a pinch or wish to get Yuugi another turn quickly. All that said, Storm on Mt. Ooe is one of the weaker multi-target spell cards in the game since it lacks status infliction, debuff and defense-piercing. Also be aware that although she may be a walking cannon and is quite capable of taking a few blows, coming under magical assault will very quickly tear through her.
A speedster who really does her job well, Aya is your other choice outside of Sakuya for helping your party get a move on. Her high speed and low-delay attacks allow her to deal with foes quickly. More specifically, Peerless Wind God bears the distinction of buffing herself while attacking, meaning her assault only grows in frequency. Once her own speed is buffed up, she can quickly use Sarutahiko's Guidance a couple of times to leave a buff on her allies (initially she is unable to do this, but very quickly starts gaining the ability to use it more and more times), and then beat a hasty retreat before she gets sniped or runs out of SP. If she's in a situation where she's not in any direct danger, then once Aya gets going, she can get your whole party moving at high speeds and support them while dealing out some supporting - although not major - damage herself; just be aware that even with her good SP growth, optimum use of her abilities burns through it very fast, especially early on. Since Aya boasts the highest SPD growth rate in the game (her SPD growing even faster per level than Chen) she can buff allies incredibly quickly, although keep in mind that her SPD buffs are single-target as opposed to Sakuya's, which boost an entire active party's SPD at once with slightly less effectiveness.