Sometimes I think I should have my girl status revoked...I don't wear make-up and I've never had a purse. YIKES!!!
That said, I have used both a fanny pack and a backpack at WDW and many other places we visit. When DD was younger, I used a full size backpack to carry a change of clothes, food, first aid kit, water, etc. Now that she is older, depending on the place we are visiting, I take either a kid-sized backpack or a fanny pack.
If it's a day-long adventure, the kid-sized backpack will do. It has bottle holders on either side for water and a small front pocket for camera/waller/keys or things you get frequently like chapstick. The main body comfortably holds a change of clothes for her (in case of spills or splashes) and the first aid kit as well as rain ponchos for both of us and snacks. Because it's small in size, you have a hard time overstuffing it and making it too heavy to carry.
Our backpack came from a Hilton Hotel where they give them out to kids as part of the Vacation Station giveaways. It's really sturdy and very handy.