My vote is for the NextCare brand (by 3m) medicated bandaids. The rubbery tape stays on a long time and flexes with your movements, they breathe well, and already have the anti-biotic on the pad. What could be better? Also they don't seem to leave glue residue behind like some others I have. I have one in my wallet right now.
After the wound starts healing I switch to New Skin liquid bandage.
I used to just ignore minor cuts and scrapes (if they weren't too messy), but I found that treating them makes them heal a whole lot faster, which is a convenience in the end.