Chris,
For many years, my mother had a plaque on the den wall:
A boat is a wood-lined hole in the water,
Into which you pour money
Since you're in Indianapolis, you've probably seen the TV commercial for the outboard motor repair trade school: One graduate brags that he was flown to Jamaica for five days to repair an engine... And that is you paying the bill! 
I'm pretty much with Chris and Giles on this one: Rent, or check into time-share ownership. Conde Nast Traveller magazine just had an an extensive article on Carribbean charters, with names of brokers, agencies, and rates.
[DISCLAIMER: My future sister-in-law works for one of the Conde Nast magazines.]
The exception to owning would be if you get a boat with less that a 102 inch beam (about 28 feet max), keep it on Lake Lemon during the summer for weekend use; and then trailer it to Florida in October or November for the run to the Carribbean, reversing the trip in the spring back to Indiana.
You can go up to a 10 foot beam (about 36 feet length) and still trailer the boat back & forth; but it would have to be on a flatbed with WIDE LOAD placards and an escort car -- Very Expensive.
There are other questions that you need to ask yourself if you buy or rent a boat:
* Is it going to be just you and your wife; or will you be bringing others (kids, in-laws, friends, etc...) with you?
* Will you be using this for just diving, or other water sports? It takes a LOT of horsepower -- and fuel -- to push a cabin cruiser fast enough to go water skiing! (Been there, done that, have the T-shirt with a 25 foot Bayliner)
* How fast do you want to go when cruising from island to island? (See above re horsepower & fuel consumption B) )
* Outboard, I/O (stern drive), or inboard? Outboard weighs the least and gives you the most room on the boat; inboard allows you to use larger engines &/or diesel but takes up the most room; and I/O is a compromise that is falling out of favor, now that large 4-cycle outboard engines are available.
* Security: It's not like you'll be keeping your boat on the Chesapeake Bay while you're back home in Indiana.
I do disagree with Giles on one point: You can easily take a Panasonic ToughBook laptop computer aboard with you, as the motherboard has a silicon coating to make it corrosion-resistant.
In any case, your best bet is probably a bareboat or wet charter of a 32-36-40 footer, big enough for your compressor & nitrox gear... And then find another couple with similar interests to split the tab.
I'm not sure if this subject has ever come up, but if you could buy and outfit your own dive boat what and how would you do it? Buy new or used? RIB or hard boat? Also, where would you put it? Anybody already have their own boat? Are there any fellow Captains on Wetpixel?
My wife and I visit the USVI and the BVI enough that we are giving it some consideration. Right now we own a small boat that can carry us to dive sites and carry tanks but that's about it, no accommodations. Things I would like to put on board would be minimally an air compressor, GPS/Nav, freshwater shower. I am a cert. gas blender, so I would at least add a Nitrox stick. Not sure how you could install a computer and have it last in salt air?
(cut)
Chris