This was my very first liveaboard. You will have the time of your life. It is totally like camping at sea. There is very, very little privacy, but hey, you're there for the diving.
The worst part about the trip was the crossing. Even if you have never been seasick, take something....prior to departure. Eat a light meal that evening, avoid alcohol, and keep yourself well hydrated.
You will not need much more than a couple of pair of swim trunks, t-shirt, and the usual personal items. You are limited to one very brief shower a day. That's really not a problem. Just turn the water on for a few seconds....then off. Soap up....then turn the water back on. We found that you can also take a bath in the sea with Joy dishwashing soap. Remember space is very limited. Whatever you take, you have to sleep with!!!!!
You will have port night in Bimini, so save something fairly clean for that night.
Hope that you have a wonderful time. I did