At other parks I carry a 6"x9" bag. Just enough for all our wallets, phones, sunscreen clip on, cooling towel ties on the side, 3 cheap ponchos, ziplocs, pressed penny book, and coins. It's easier for us to throw it all in the same bag one the way, I go through bag check, while DH goes through no bag line with DD9. No one has to juggle putting everything back in pockets at the security exit. Disney is the only place I go with a small backpack IF DD9 wants to have an autograph book.
Always, always bring a bag. And pack some "survival gear" (aspirin, water, poncho, charger, credit card/cash for emergency, different shoes/flip-flops, Band-Aids for blisters, etc.). Also pack a Zip-Loc bag for your phone/electronics both for water rides and in case it rains. You're almost guaranteed to buy something (c'mon, it's Disney) and it'll be nice to have a bag. I'd suggest a backpack, but a shoulder bag works too. You don't want to have to carry anything if you can help it.
I'm with you Tony. I've actually brought shorts that had nice deep pockets so I don't have to carry a bag. Now I don't know when the op went but I can't imagine a bag check with only three people? seriously. folks with strollers, lunch bags etc all take time to get checked.
Now I carry my Atm card, id, lipgloss, cell phon and a small pack of tissues and that's it.