This is totally not the point of this thread but I just wanted to throw out that I actually had a really bad time last time I went to Disney in Florida because of the bathroom situation. If you're going with your girlfriend only, you should be fine, but I struggled because I was with people I wasn't out to, but I couldn't make myself use the women's bathroom. Not only was I not comfortable with it, but I know I'd get weird looks, if not questioned. I expected, hearing that they were so LGBT friendly, for there to be a unisex or family bathroom that I could use, but no, only huge multi-stall bathrooms. Maybe they hide them or something because I never found one. I actually meant to send them a letter about this and I forgot. Anyways, if it's just you and your girlfriend I bet you'll be fine.
As for more on-topic; I'd say just get a binder and a rash guard or T-shirt. At every waterpark I've been to, there's tons of people walking around in rash guards or wet shirts. They're great because it's sun protection that you don't have to take off on the slides and stuff. For the binder, from what you've said, I'd recommend an underworks 997 or something like that. For packers, I don't know anything about the chlorine and the packers so I can't help much :/