zepher,
I can answer a couple of your questions, but I only went to the Carib for a split bid, 3 weeks STX, then 3 weeks HYA. Cape Air provided a car and a condo while I was in the islands. (There was another pilot who worked the opposite 3 weeks who I "time shared" the car & condo with.)
How much to bring depends on you. I'd pack light. Even for 5-6 months. You won't need a coat. Or even a sweatshirt. Plus you have to either schelp it all or mail it back and forth.
Keep your stateside DL.
I dunno about a car. Its essential everywhere, except maybe Isla Verde (SJU). I'd guess buy one. Renting has to be cost prohibitive. Shipping even more so. Check craigslist to get an idea what's available.
You get a week off and 40 hours pay for transition. One trick is to pick up as much OT during that week as you can. Pay in the Carib is $18/duty hour for new hires - with OT in PR after 8 in a day, 8 in the last 24, and after 40 in a week. PR has the best work rules, due to local laws.
As far as going north in summer, seasonal rentals are very pricey on the cape. I pay $1500 a month for a 3 bedroom home year round, the house next door rents for $2000 a week in the summer. If you don't have a family or a lot of stuff, you can certainly find a roommate situation for a reasonable amount ($500-$1000/mo depending on location and size).
Keep in mind there are new EAS routes in upstate NY and now Lebanon, NH, and Rockland, ME. I would expect those cities to be available to new hires for year round flying.