I usually bring a small backpack with me. I find that more comfortable than having a purse on my shoulder all day, and it gives me a place to stow my camera, sunblock, kleenex, light sweater, rain poncho etc. You can just keep it on your lap on the more tame rides. The bigger rides all provide a place to stow your stuff, either in a secure net on the ride vehicle or in a little cubby on the loading platform. There might be one or two rides (like maybe Space Mountain, I think?) where there isn't really a designated spot, but I just put the bag on the floor with the strap around my leg, and that is perfectly fine. All you really need to worry about is remembering to take off your hat or sunglasses so they don't fly off :)
All Disney transportation within the resort is free, and if you stay in a Disney hotel you'll get a free Magical Express bus ride to and from the airport. Fastpasses are also free - anyone with a park ticket can get them. I say this because I have often overheard comments from park guests who think that you have to pay extra to get Fastpasses, but that is NOT the case.
I would highly recommend getting the Birnbaum Official WDW guidebook and reading it cover-to-cover. It will tell you pretty much everything you could possibly need to know.
Thank you. That's a good reminder, to bring a rain jacket just in case.