Slow, Fast, Board, Computer

Congratulations on joining the ranks of  OTB tourney players! :)

Very good question => Nearly all standard time control based  USCF games start at G/30 going upwards to G/120 with a  time-delays/increments starting at 5 seconds going up to 30 seconds or more.

A good way to train for this is to play both online and OTB with a 5-second time delay as it forces you to fight for a win using chess  and not rely on race-condition cheapos for  flagging opponents (which is fine online and in blitz, but detrimental to your progress as a good slow-game player)

I'd recommend  nothing faster than G/30 w/5 .... G/45 with 5 sec. delay  would be ideal and if you can invest the time, G/60 to begin with.

I know many players who prefer a 45/45 time control (45 mins, 45 second increment/delay) as part of their training regiment.

The reason why slow games help you improve is that 

a) You are putting in substantial skin into it (2-3 hours of your day is gone if you waste it all away on a stupid blunder that you rushed into!) ... thereby making you as serious as you need to be.

b) Spending more time/move helps your brain absorb in the patterns over the board and help transition it from short term to long term memory. This in turn becomes valuable when you see similar positions later ... your brain can recall things faster and you tend to make more accurate decisions / calculations the next time around.

The proof is in the pudding => I can recall a few G/120 tourney games I played 2 years ago move for move given how memorable they were and how stung I was in losing them in the 11th hour but I can't remember any of the bullet games I played a few days back. :)

c) With slow time controls, you CAN'T make excuses for missing tactical shots ... which should be where 90% of your study/effort in improving must currently be.