I'm in the midst of playing this game, and I thought I'd first give you a basic outline of what to expect.

This game is based around four major aspects:

1. Hitting enemies' weak spots (elemental)

2. Getting enemies to hit your strong points (elemental)

3. Use 1 and 2 to build up your MP to use powerful super-skills.

4. Keeping Corona, Tokino, and Touka (the protagonist) alive while still keeping their levels up.

There are a lot of other points and complexities, but it pretty much boils down to this. In most of the battles of the game, having any of those three die on you is an automatic game over. You don't want them dead and you don't want them weak, so by necessity you have to follow the advice in 1 and 2, lol.

Characters (through chapter 14 of 21, anyway):

Touka: The protagonist. His specialties are massive damage dealing (the highest in raw numbers in the game), incredibly weak defenses, and the ability to use his field skill 'sharing' to take on the elemental barrier of an ally of his choice. Until you manage to get his defensive skill, 'mikiri', using him pretty much requires that you pair him with Kumi, for her defensive support skill 'kabau' (protect). Once he has mikiri, you can choose not to use sharing, instead relying on him using that skill (while you have MP remaining) to survive enemy attacks. There is literally no one, including Corona, who does more damage than him before elemental bonuses.

Corona- The dragon-girl who is the source of a lot of the story's troubles. If you think of her as a pure power type, you wouldn't be wrong... except she has two really standout skills: Dragon Breath and Dragon's Heart. The former is a skill that completely strips all the enemies in a unit of a layer of barriers in an instant (at a huge cost in mp) and the latter is a skill that restores 1 LP to any single unit. The latter is basically a resurrection field skill and Corona is one of only two characters that possesses such a skill (including Tsukioka, the extra character from the append disc). She also has a lot of HP and relatively few elemental weaknesses, which is helpful in keeping her alive.

Tokino- The redheaded heroine. A Black elemental attacker with medium striking power. She is the weakest of the three main characters by far, due to her mediocre HP, mediocre attack power, and generally medium capabilities. Nonetheless, she isn't worthless (no character is, considering how few you have), so don't forget about her.

Kumi- A Green elemental blonde loli wielding a halberd/battle axe. Her elemental barriers are extremely weak... but in exchange she has a ton of HP (#2 overall, behind Ryuuichi) and the skill 'kabau', which will save Touka's life until you get mikiri for him. After that, I seriously suggest just removing the skill, because it can only get her killed in most other battles, lol. Use her for decent attack power and the fact that she is one of only two green elementals.

Kaname- A Blue elemental who wields a naginata. She is an odd one, with a combination of skills that allows her to both weaken enemy attack power and deal high amounts of damage. Because she is such a straightforward unit, there is nothing to really talk about except to say that she is one of your two valuable blue elementals, so be prepared to switch her around between units a lot. Her barriers are about equivalent with those of Tokino in terms of both HP and elemental coverage.

Akane- Another damage powerhouse and a Red Elemental. She has the advantage of starting out with a powerful damage-dealing skill that strikes whenever an enemy attacks her, as well as the highest raw attack power of all the Red Elementals. On the other hand, she is so straightforward - similar to Kaname- that there is really very little give to how you can use her.

Akechi- A powerful Black Elemental, who wields a bow. He is one of the three male fighting characters. His skills include a number of ones that weaken the enemy or strengthen his allies, as well as a field skill that lets your entire army receive an assault as if they were the ones doing the attacking (meaning your side strikes first each turn).

Eri- Similar to Kaname, a straight-out power type and Blue Elemental. Unlike Kaname, she doesn't possess any significant support skills, so she basically exists only to do damage, and she has the second lowest hp, behind Touka. Using her is a bit difficult, as she tends to be vulnerable far too much of the time for comfort. Take particular care with her when facing her off against an enemy.

Anastasia- One of the three Red Elementals, she is most useful for her support skills, which range from doing damage to every enemy as they attack to weakening the enemy against Red (thus allowing her to do more damage). She has relatively low HP and tends to take hard hits because of her barrier setup.

Ryuuichi- A White Elemental who wields a lance. Two major points to be aware of are his counter-barrier skill (which comes default with him) and the weakness of his barriers. If you increase the counter-barrier, you can shave off huge amounts of enemy HP just in exchange for taking damage. He also has the highest HP in the game, so his large amount of weaknesses is actually an advantage if you you use him right. Do remember to deactivate the skill once the enemy's barriers are down, though... as it doesn't do LP damage. His damage rate is about identical to Fumi's.

Asuka- Ryuuichi's adopted daughter and one of the two Green elementals. The thing you need to pay attention to with her is her defensive shield skill, which lets her defend each ally against a percentage of damage from enemy attacks, and her healing command skill, which heals large amounts of damage instead of attacking the enemy. When you are focused just on keeping your allies alive, these skills can be a lifesaver.

Touka- The famous heroine from Ayakashibito and an append disc extra unit (Black Elemental). She starts out powerful and remains so throughout the game, simply because she starts with a skill that heals her and boosts her attack power, as well as both a Black and a White attack skill. This gives her a range of options that most units don't have until later in the game and allows her to remain useful throughout.

Miyabi- One of the two main heroines of Haruka ni Aogi, Uruwashi no (Red Elemental). She is about equivalent with Anastasia for attack power and defensive capabilities, but she starts out with two elemental attacks (Red and Blue), as well as a number of counter support skills. She remains fairly useful throughout the game so far, but not excessively so.

Tsukioka- Append disc character and White Elemental. She is amongst the weakest of all characters in terms of attack power, and her only real advantages are the LP restoration field skill and dual elemental (White and Green) she possesses from the beginning. She does possess a healing support skill, but the conditions for it mean that characters with low max hp have difficulty finding a use for it.

Edit:

Yumina characters: Ayumu, Ai, Kirara, and Yumina join late-game. Compared to existing units, they are somewhat lacking due to their ability to use only one element. Nonetheless, Kirara's teleportation and Yumina's song field skills are immensely useful. Ayumu is fine as long as the enemy isn't strong against Red, as he has really powerful attacks.