Personally, I like 11 players.
One EH and a rested relief pitcher. I like my EH to be my backup catcher. Many leagues and tournaments allow the EH to enter the game in case of injury.
12 can work for very game intense tournaments.
If you plan on a tournament like Cooperstown, where you play 2,3 or more games a day, then I would probably pull in 2 or 3 extra pitchers.