We always use a backpack. I bring two or three same-colored (usually bright green) bandannas and tie them to the strollers, hooking them through the loops of the backpack to keep it on the back of the stroller. These banadas also help in quickly spotting our strollers among the many identical ones. The MK and AK strollers seem to support our backpack when we just plop it on top of the canopy too.
As for what to pack, we had a 5, 4, 3 and 20 month old with us last time. Essentials in the backpack included sunscreen, wipes, 2-3 diapers (we would just restock every time we went back to hotel), 1-2 shirts that suited all 4 kids (as they're close in age the shirt would either fit the 4,5 or be a bit big on younger ones, but work nonetheless), and 1 full change for 20 month old (if we were going to be out of hotel more than 4 hours at a time). If it looked like rain, we'd also pack our rain ponchos that scrunched up really small. Also 4-8 juice boxes and 4-8 pre-packaged bags of ritz sandwich crackers or fruit chews or something like that so if kids got hungry that would tide them over until we got through a snack line or whatever other line we might be in.
Often, my kids would dress in their bathing suits with clothes over top. If they spilled on their shirt, they'd either change or just take off the top and go with their bathing suit and shorts. This worked well for our 20mo as she would really relish those Mickey bars!
I also have a camera bag that has a pouch for extra film, keys, our passes, and dh's wallet. The bag is about the size of your average soft-sided lunch pack. I would take that on rides with me and just leave the backpack with the strollers. I figured if someone wanted to steal my kids' shirts and diapers that stuff was pretty replaceable. We really never had a problem though; however, be aware if you have bought stuff from Disney and have Disney bags. We had purchased a stuffed animal Minnie Mouse (That we took with us on subsequent rides for safekeeping) but had used a Disney merchandise bag to wrap up some smelly, soiled clothes (i.e., dd had pooped in them -- she was potty training at the time). We'd left it sitting on top of our stroller and when we came back it was missing. We chuckled at how karma works. Whoever took it, must have thought they were stealing some Disney merchandise. Imagine their surprise when they opened the bag to discover their "surprise!" (pooped-in clothes!).