I also wondered about what to bring when I first brought our son to daycare. But, as it turned out the best thing to do is to bring them as many diapers as they can store. With regard to the formula, I pumped breast milk and brught them the # of bottles that he would eat. Same thing once I switched to formula.
As for them using your diapers on other children...I don't think it'll happen as often as you think. Just yeaterday, our son ran out of diapers and they usually tell us WELL in advance, but they didn't. So, they borrowed one from another child. It can happen, but it wouldn't bother me if someone had to use one of our diapers for another child - ONCE in awhile. Just the other day a lady in a restaraunt asked if I had a spare diaper - she didn't realize that her diaper bag was empty.
Have faith in your day care center and the teachers in your child's room.
Good luck and be prepared for a hard time leaving your little one the first week or so! I promise, it does get easier. I swear it does. Lol.
T.