Abbymcd,
Congrats on being newly certified and gravitating to liveaboard divng. My first trip was in 2009 on the Kona Aggressor. I'd lived in Hawaii for 10 years and had dove the Big Island (Kona) multiple times and thought it might be a bad idea to be diving basically the same kind of reefs I'd been diving forever.....but in the end not only was the diving amazing despite me being there before, the liveaboard lifestyle was outstanding. It occurred to me on the night dive on day 1 of my Kona Aggressor trip that I would never do a land-based dive trip again. Not unless it's a dive resort that I specifically want to go to (and there aren't that many).
I went to Papua New Guinea in 2010 and that trip was flat out life-changing. In 2011 I did the Tropic Dancer in Palau. Then in 2013 I went on the Wind Dancer in Cocos Island. The Wind Dancer required some advanced diving, and Palau at times required some experience diving in strong currents. But Papua New Guinea and Kona (Hawaii) were both comfortable environments for divers of all skill levels. In October (2014) I'm returning to Papua New Guinea and diving the same itinerary I did in 2010 but I'll be going with the Febrina.
I have not done liveaboards in the Caribbean but I agree with other divers on here on pretty much everything. Having your own gear is a good idea - if you want a good deal on name-brand gear (that has the same protections as a local dive shop with regard to warranty) - try leisurepro.com - you'll get a lot more out of your trip if you have your own gear. But if you need to rent most liveaboard operators will be able to hook you up.
I've found you need to find "your style" of diving. From Kona (Hawaii), Papua New Guinea, Palau and Cocos Island....I'm pretty sure I've learned that "my style" of diving is the Coral Triangle in the South Pacific/Indian Ocean. Papua New Guinea, Indonesia (multiple areas), Solomon Islands, Fiji......those far away outposts are by far my favorite. Mingling here and there with villagers, diving areas that are not hit by as many people and you don't see many boats.
Palau's "style" was that of a pretty far outpost but it was very well developed and had a fair bit of boat traffic. The diving was outstanding - but I call it the "south Pacific experience" but with more people and commercial development. Hawaii's style is very much like that too but the reefs are lower profile and more of an encrusting substrate that creates a very unique marine environment. It's not inferior necessarily - just different.
Cocos Island's style was a very far flung away from society but it's more rugged reefs, diving from panga's and it's ALL about the sharks. I was happy I had the experience but I would definitely call Cocos Island my 4th favorite of my 4 liveaboard trips. It was a lot of fun though so that's not to say it's bad. But it's probably the most "advanced" diving I've done.
Papua New Guinea (north New Britain Island) is the only spot I've made the decision to go back to. I've always relished the idea of going to new areas and Alor (east of Flores in Indonesia) was on my list, but this destination has all the features I need in a dive trip.
I definitely like the Aggressor/Dancer Fleet. I've used them for all my trips and if they hadn't discontinued their service in Papua New Guinea I'd definitely do the Star Dancer in PNG all over again. I will definitely be a repeat customer for them in the future. But I've heard nothing but good things about Febrina and they're the only show in town for North New Britain so I am confident this new experience will be a good one.
I've also shared rooms and on one lucky occasion on a fairly empty boat (Tropic Dancer, Palau) I got my own room. Febrina in PNG I was able to get one of the two "single" cabins designed for 1 person - so I'm happy about that....considering it wasn't that much more to get the single cabin slot. But cabin sharing has not ever been an issue. I've had some great roommates, and one sorta bad one....but even the "bad" one and I got along fine. If you want the room to yourself - just use it for a nap during a dive your roomie is on.....no big deal. I usually just share a room - it's totally not a big deal...you're just in there to sleep anyway. In fact - half the time I fall asleep in the salon area anyway with my glass of wine.
I hope this has been informative to you - feel free to ask any follow up questions you have.