The Moorings and Sunsail are large charter companies located at the same dock
in Marsh Harbour, both a part of TUI marine
TUI travel. You can fly directly into Marsh Harbour. It's a short cab ride to the base. I've traded time or chartered there about 10 times now.
Cat or mono depends in part on how much space you want and what you are willing to spend. Cat's tend to have shallower draft
which can provide more anchoring
options and more flexibility with a few channels such as going into Little Harbour.
The Moorings and Sunsail both give prices and schematics of boats available on their websites.
I owned a boat in the VIs. Both locations have their pluses and minuses. What I like about the Abacos, Bahamas is the many uninhabited islands one can anchor
off of and enjoy. Catching your own lobster dinner ain't bad either.