I am one of those who is guilty of bringing big, honkin' purses/messenger bags with me when I find one I like, and overstuffing them, although reading the other posts here, it sounds like I am bringing all the same stuff everyone else is. For some reason, it always SEEMS like I have more things. I cant carry a small purse - there is just no way - and I don't use a backack because I like to be able to reach into my purse at a moment's notice and grab something if I need to, rather than take off the backpack, remove the item and strap the backpack back on. Last December, I brought several disposable digital cameras which were quite bulky, as well as a small 35 mm camera and accompanying film, AND a disposable video camera. All of this required a big bag to put it in, with a long shoulder strap. I also had to carry other essentials in the bag, too - the hand sanitizer, the wipes, the sunscreen, Motrin and other medicine, the small hand lotion, the the tissue, the cosmetic items, the wallet (can't forget that!), the cell phone, protein bars, the extra plastic Ziploc bags, the glasses and sunglasses cases, the hairbrush, etc. All necessary stuff. But it weighs me down. Still, it is better to have it all in one bag rather than having two or three different things slung over my shoulders, going every which way.
The one thing my big Disney bag did not have (it was styled in the Mouse of 1000 Faces motif that was popular in the '90s) was a proper way to secure it. It did not have a big zipper to close the whole thing up. It had a very weak strap that snapped it closed, so it was never safe from flying open at a moment's notice.
So I suggest that whatever type of bag you bring, make sure it ZIPS closed. You need to make sure small items are secure inside and won't go flopping out all over the place, and you need to make sure you can get into the bag easily and quickly if you need to pull a camera or a ticket out in a split second. As for purchases like souvenirs, IF you are staying at one of the Disney hotels, you can have your items sent back to the hotel for you for free, so you don't have to schlep them around the park. If you are not staying at one of the three Disney hotels, you can get a very expensive locker on Main Street for the whole day and stash some things in there, but you would have to keep going back to the locker to leave things in it as you bought items, and if you are nowhere near the locker in the park, that can be a pain, and you end up carrying your items for much of the time anyway!
On rides I just swing it forward a bit and it's good to go.
. Everyone makes fun of me but it's the best thing I have found to carry everything and not get in the way. I also have a lanyard to carry my water bottle. 
