I take a variety of purses. Last trip I took two different type Vuitton bags but I only used them at night when I knew we were going to dinner and I wouldn't be carrying them for 10+ hours. Since they have light leather, I don't ever risk them getting wet, and trying to pay attention to that all day is an annoyance that doesn't really have to be.
In the parks I bring either a nylon drawstring Nike backpack, since it's super lightweight and water-resistant, and I can wipe off spills in a second. I also don't feel bad/nervous if I have to put it under the seat/in a holder/etc. Sometimes if I'm particularly nervous or the ride is rough I'll put my foot through the straps (RnRC). On these rides I also knot the straps at the very top so the bag won't open, but I've never had an issue with that, it's more preventative!
I also use my Gucci beltbag, which is pretty much a fanny pack but styled a bit differently. It has two rectangular front pouches, one zippered & one Velcro. It holds a surprising amount! It also has a back pocket than runs the length of the bag and is absolutely perfect for cards/tickets/cash/a few keys/receipts. I don't use a wallet with this one, since I can keep it all back there and right against my person. I like the belt bag personally, as it snaps on and I never ever have to worry about it falling off, setting it down and forgetting it, etc. If I go on a ride I think the Velcro might be compromised, I take what's in there and put it in the zippered portion against my belly. I love love LOVE that I never ever have to take this off on a ride, I just seatbelt over it! It's big enough to hold my iPhone, digital camera, a few tubes of lip balm/lipstick, a small portable sunscreen, face powder (I don't carry this in Disney though!), hair ties, etc. It really does hold a ton! It was expensive, especially for a glorified fanny pack, but I really get so so much use of it that it's already paid for itself. Not having something hanging on your back in the extreme Florida heat is a blessing!
My rule of thumb is the lighter the better - at the end of a long Disney day, what is ounces feels like pounds!