The Caribbean is a big place, it might help if you narrowed down your geographic area a bit. But here's my story - I opted to purchase a used boat and found that used ex-charter boats are a good deal (n.b. that this is a heavily contested point in this forum and many here avoid ex-charter boats like the plague). After checking out the market on the internet using sites such as Yachtworld
I found that the BVI had the largest selection of well-priced boats and flew out there in August during the hurricane season, i.e. when the prices were still low. I looked at many boats [about 40] and ended up getting a 3-year old 43" Jeanneau from Sunsail's Platinum fleet.
The boat is sufficiently equipped as an ex-charter boat for normal travel without having to add or repair anything, since my nasty-tempered Surveyor ensured a good final condition. The BVI is rather expensive when it comes to labour, chandlers and electronics, but St. Maartin is only 90nm upwind and offers a lot of services and supplies - all duty free! You can check out the prices and availability online at two of the biggest Caribbean chandleries Budget Marine
and Island Water World
. My purchases at Budget Marine probably helped put the owner's kids through college - but they were very friendly and helpful and I would recommend them unconditionally (on a side note my freshly purchased dinghy and outboard was stolen the night of my purchase there - but that wasn't their fault and they gave me a discount when I went back the next day to get another!).
Regarding getting electronics through customs I'm sure that others will explain how they managed the "yacht in transit" part - I only have a vague idea of how that is done as I haven't had to do it (yet).