Okay, first off, there is no best move, all moves are situational. Second off, there are two main builds to each class (hot/cold hydro, physcal/poison bio, and shadow/electric psycho). But if you truly want my opinion on each of the six, I shall deliver:
Physical Bio: Shadow Blend, it makes your vicious strike/slash extremely powerful if you spec in speed, it makes most enemy miss with their attacks, it's probably one of the best buffs in the game.
Poison Bio: Envenom, you can stack 8 of these on an enemy (more if you somehow attack twice in a row), these stack up to some major damage over time.
Shadow Psycho: Havn't gotten around to playing him enough to decide.
Electric Psycho: Shock Therapy, very high damage (330% instinct), is spammable (3 round cooldown with ability to equip 3 times), and is cheap.
Cold Hydro: Well, shatter is the obvious answer here, it is the key to playing the cold hydro. You stack 3 ice debuffs on and then shatter them to do amazing damage. But my favorite debuff is also Flash Freeze, it's a free two turn stun that can be equipped twice.
Hot Hydro: Decimate is clearly the best here, it has a good direct attack of 280% strength and it scales with focus (meaning the more focus yuo have, the more powerful it is), then it's damage over time is amazing when you upgrade the damage over time passive ability in the tree.
Shadow Psycho: Offensively, my favorite is Nightmare. Fully powered, it deals 520% instinct. Its healing buff can either be dispelled with Shock Therapy, or combined with Corruption for continuous shadow damage. Defensively, Free Will is probably the best healing spell out of all three classes.
It isn't a lucky hit. WHen you have enough piercing (you get a increase in piercing every level up anyways) you always critical on those lower leveled than you, the more piercing, the higher the chance to critical and the higher the damage when criticalling. If you notice when you mouse over the piercing descriptions, they all say xx% chance to critical, with xx% more damage when criticalling, and xx% more damage normally against an opponent of the same level. So the higher the level, the higher the effects of piercing. So against a level 9 training opponent in Z1 with a level 30 with maxed out piercing, you have a hundred percent chance to critical, and when you critical it will do more damage.