Do you own a BC, regulator and wetsuit? I'm assuming that you are planning on taking your mask and fins, right? Those are personal items which need to fit exactly right, and usually aren't rented. Bring a snorkel too, even if you don't dive with it. Need to do something just before you fly home, right?
I fly with all my gear (except tanks and weights) because I have put a good deal of time into setting things up exactly like I want them (backplate, wing, etc..) and I take good care of my regulator (recommended service, rinsing, etc..). Some people use light "travel" versions of their home equipment to save weight when flying - I don't do that.
However, if you don't have these things now, I wouldn't necessarily buy them just because you are going on a trip. Sure, if you plan on diving a lot it makes sense, but it looks like you are fairly early on in your diving career, so you might not want to make a big investment before your first dive trip. Also, remember, if you buy a regulator, you are now responsible for regular maintenance...
Hopefully, you will be diving with a reputable dive shop who will provide a good quality BC and regulator, and possibly a dive computer.
Have fun! I hear Belize is terrific...
Mike