Most of this written by limabeanbreath.  All the skills mentioned are the ones that come most recommended.

Rohane:
Damage Increase: Your average damage to the enemy increases.

Critical Hit: Hit for up to twice as much damage with each critical hit.  Chance to have a critical hit increases with more points...

Innate Magical Defense: In the higher levels, the monsters try to spell you. Without a very high magical defense, Rohane will be incapacitated every battle.

Innate Melee Haste: Kill your enemies before they kill you.  Will shorten wait times between turns.


For Mipsy:
Direct Damage: This one is the boss killer, it does 100 damage every turn when maxed out.

Innate Casting Haste: Kill your enemies before they kill you.  Will shorten wait times between turns.

I
nnate Melee Defense: Mipsy has a low amount of hit points, so to keep her from dying so easily, max this one out.

People are split over these.
Group Haste: Maxed it does 38% speed, but potions can do more.
Group Direct Damage:  Maxed it does 64 to all enemies.
Damage Shields:  I am not sure what this one does at any level.  Some people like it and say it is great because not only does it protect you it hurts the enemy.


Talinia:
Damage Increase: She won't hit very hard unless you max this one out.

Group Direct Damage: She'll hit four enemies nearly all the time for between 50-80 damage, very useful later on.

Innate Melee Haste: Kill your enemies before they kill you.  Will shorten wait times between turns.

Innate Magical Defense: Same as Rohane

People are split over this one.
Shockwave: This is supposed to stun everyone but some people do not see any effects.


Velm:
Group Healing: Heals everyone for 90hp. Much better than direct healing because if a person has lost more than 90hp, they're probably dead or will die. Also, it's much safer to heal everyone when they've only got 50hp missing rather than 120 or whatever. This'll heal everyone in one turn.

Innate Spellcasting Haste: Kill your enemies before they kill you.  Will shorten wait times between turns.
Innate Melee Defense: Same as Mipsy's.

Celestial Hammer: This will hit for 50 damage maxed out every time, and stun for anywhere from 1-3 seconds. Whacking an enemy with this can stop them for long enough so they don't even get a hit in before they're dead.

People also like group protection.