If you know going into the season that you're going to be calling up someone that could play immediately, is it best to wait (what is it 10 games?) to gain the extra season of the minimum? Or do you just move him up before the season starts?

I think its 20 minor league days to save the extra year.
You could cost your self a few games waiting for a player to get called up.
if he is < 21 or maybe 22 y/o and only has 2 pro seasons I might wait the 20 days. but other then that I don't see an advantage having a player in aaa who could be playing everyday at the ml level.  big point being if he is playing every day

My rule of thumb: if your minor league season starts on a Wednesday with the AM game, do your call-ups the following Wednesday after the AM game.  It's an extra cycle or two, but it takes the counting out of the equation.

If you're trying to win games and make the playoffs, call him up when the season starts.   Worry about July 2016 when the time comes.