California Baby is a good brand and you can get it in Target in the baby stuff area. We also used Aveeno and Nuetrogena. All are very good, but I liked Cali baby. A little of it goes a VERY long way. Don't forget to protect little ears, feet, fingers and that cute nose! Be sure your umbrella has a HUGE shade; there are companies here that will rent out the Citymini's. Although I love my Britax, the Citymini's aren't bad for the rental. Disney's strollers suck for newbies. Layer the baby's clothes so you can adjust for warmth, since May can be a little weird weather-wise. The other thing that I couldn't LIVE without were gauze swaddle blankets. I would put them over my stroller for xtra protection, and they were light enough that they let air in and would not sweat the baby. Plus, you can swaddle the baby at night with them. I did bring "cheater swaddlers" - the ones with velcro (Halo brand?). Those were handy at night.
Don't be afraid of bringing TOO much, since baby clothes take up little room. Also, if you are a cloth diaper mama, there are cloth diaper services that handle some of the hotels at or around the Disney area. The cloth diapers prevent diaper rash, but that's a whole 'nuther topic.
Oh, and Florida is a "right to nurse" state (or, as I like to call it, "a right to whip it out" state!). You can nurse anywhere you please - I've done it on Mansion, at restaurants, at Nemo - everywhere. No one has every made me uncomfortable about it, ever. The baby centers though are the nicest. The staff at every baby center has been nothing but nice, and while the rocking chairs aren't really comfy, the centers do provide a nice air condition break. Take advantage of them!!!