Try to carry the minimum! If I can get away with just the contents of my pockets, I do. Depending on the season though, sometimes you need a bag big enough for a jacket. We almost always carry some bottled water, too.
DH mostly wears cargo shorts at WDW - so I'll have him carry the camera. I also try to wear cargo type pants at WDW -esp with zippered pockets.
When I must carry a bag, I make it as lightweight and compact as possible.
In the past, when I had to carry a bag, I used to use a small backpack. Something like the Jansport half-pint (though the half-pint itself had zipper issues; the zipper will unzip if the bag isn't fully zipped every time, and it's easy to lose stuff if it opens up), or maybe one of those cheap nylon zip-cord bags (the strings hurt after a while if the bag is too full.) Backpacks free your hands, but they have to be rotated or removed on every ride. Any time you remove your bag is a chance to lose it.
More recently, I got a small Dooney and Bourke shoulder bag. It's perfect. It's like this, but with a long shoulder strap:
http://www.dooney.com/OA_HTML/ibeCCtpSctDspRte.jsp?section=47451
Anytime you enter a park the bag has to searched. If your bag has multiple compartments, you have to open all of them up and reclose them. It doesn't take a huge amount of time, but it does slow you down. Also, if you forget to rezip anything it can be very bad. If you don't have any bag, you bypass the line altogther.
The D&B bag I have has only one small compartment - and little pockets onthe sides to keep stuff organized. one zip and security can see everything. I wear it cross body. I dont have to do anything when I go on a ride. Backpacks can take FOREVER to zip and unzip. Same thign with any small bags within the bag - they all have to unpacked and opened up.
Again, one important idea is to clean your pocketbook of everythign you don't need. You won't need your library card at WDW. Most of the time I can get by with just: cc, ID, cash, WDW ticket/room key, cell phone, times guide, tiny chart of ADR numbers. Maybe a camera,and during the day a bottle of water. Sometimes you may also need a jacket or at least a plastic rain poncho. Maybe sun block. Maybe a small square of moleskin (about the size of a bandaid) or bandaids. Oh - and if you ever need any essential medications, make sure to carry them. (epi-pen, inhaler, benadryl - that sort of thing.)
If you have small kids in your party you may need a few other items. You don't want to put anything expensive in a stroller, but general you can leave non -valuables like bottled water and hand sanitizer in the basket of a stroller. When we have a stroller in our party- we put everything in a gaint 2.5 gal clear ziploc. At security, you just hold it up. Snack/sandwich sized ziplocs can also be used within a bag at WDW.