Cool down time: Longer or shorter better?

Fast Moves:

Offense - moves with short cooldowns have slightly higher DPS and generate more energy.

Defense - moves with long cooldowns work best with the current 2 sec between defender attacks.

Charge Moves:

Offense - either VERY fast spam-able attacks (Dragon Claw, Brick Break...) or one huge attack (Hydro Pump, Fire Blast, Solar Beam...)

Defense - any move with 2-4 charges and reasonable damage works well (Dragon Pulse or Claw, Water Pulse, Seed Bomb, Flamethrower, Ice beam...). There is usually a trade-off between Speed (shorter moves are harder to dodge), damage and energy cost (less cost - more spam-able in battle).

That completely depends on the Pokémon and the move. There is no general answer to your question.

add one more point, higher dps will charge up defender's energy