Another vote for the BVI. My family
has chartered with the Moorings I think 12 times now since I was a kid. I too will be taking my first Charter very soon hoping to continue the cycle with my own family one day.
As for Chartering Companies, I would go with the Moorings. When you give the Moorings the deposit for the trip they will send you a cruising guide well in advance to make it a bit easier to plan out your trip. Make sure to ask around here when you are at that stage as most of the advice
here is fantastic regarding off beat mooring
The Moorings fleet is not bad at all, I will point out though that there are two "Tiers" of their boats. "Club" and "Exclusive". The Club tier are boats that can range up to I think 6 years old, the Exclusive (A bit more expensive) is guaranteed to be no more than 2 years old. We have taken out both options and the experience has varried. One of our exclusive boats seemed fresh on the water
and ended up having a serious linkage problem about 3 days in. I kind of tend to lean towards the Club boats as those girls have some serious miles under them, they've been "broken in" a bit. The downside is that you can get some Boats that cosmetically are just beat to hell.
Where ever you choose, remember that it is the Chartering company's business to make sure you have a great time. Pay attention during the "Skipper's meeting" (My dad would make all of us go, skipper
or not) and ask a ton of questions if you have them, the staff are quite helpful.