When I used to be able to travel light, I used to use a pack, but one meant for athletics. It sinched up perfectly at sat at the small of one's back comfortably. However, the majority of the time, I kept it slung over my shoulder. I would clip my umbrella to the pack using carbiners.
These days, with kids in tow, it's a bit different. We haven't been when the kids are in diapers, but we do carry a backpack with a sippy cup for beverages, a spill-proof snack cup (and baggies of goldfish crackers, etc). The standards - digital camera, umbrella (for more), ponchos (everyone else), sunscreen, etc. I'm a backpack fiend thanks to years of expedition travelling - so I have one for every occasion. My WDW pack is relatively small, with three outer pouches, and lots of interiors for managing stuff.
I do a lot of traveling so I tend to think a lot before I go anywhere. The goal - travel as light as possible. My wife can load up a pack in no time, so I stay in charge of that...
Carbiners can be really helpful - I use one to clip together bags of purchases. It makes grabbing your bags to go on an attraction very quick, and you can clip it to a stroller easily. Being able to clip a wet umbrella outside of a pack is also helpful.