For fatigue issues and since minors use a DH you can get away with 11 guys active as position players and 14 pitchers. I have found that even at that level I still have to have some additional pitchers on the inactive list to cover pitcher fatigue.
Some owners don't worry about the minors, I personally try to cover every level every day. I really only takes about 3 to 4 minutes to set your pitchers and rest whom you need to. The biggest thing to consider is that you have a balanced amount of starters long relievers and short relievers. If you have specific questions, use a mentor, they are pretty darn good.