Percentage chance for successful techcopy

Just make sure you have all of your overdrives when you go into the fight. If you've unlocked all the of the Aeons(is that what they're called? It's been like 8 years since I played this game) and they have their overdrives.

There isn't one definitive answer for which is the best Overdrive mode since it's dependent on the character and who you're fighting.

For grinding out regular enemies that you kill pretty quickly, Warrior or Slayer is probably your best choice since you'll be doing most of the damage.

For enemies that hit you with more powerful attacks, Stoic or Comrade might be your best option for your damaging characters whereas Healer could be used for Yuna.

I would avoid using Ally since it charges very slow. I would also avoid Coward, Hero, Daredevil, Tactician, Avenger, Sufferer, Victor, Victim, Solo, Dancer, or Rook since none of these are very well suited to grinding.

You can find a complete list of all the different modes here along with how to make use of each mode.