I agree with everything that CalebD said + some random thoughts:
Not many pleasure boats, sail or power, leaving the northeast / mid Atlantic coast that time of year.
How long? You don’t give a very specific destination and without trying to plan an actual trip I’ll pull a number out of a hat – 3 weeks.
What's the minimum you need? Food, water, fuel (typically you run the engine for an hour a day for hot water and to charge the batteries) and some means to navigate (charts and gps would be reasonable).
What’s a sailboat like? Wow! Go to www.hanse.com
select a boat and then select 360. You can view the inside and the cockpit interactively. Go to Welcome to Conch Charters, your charter provider in the British Virgin Islands
select fleet and look at the videos of the boats. Go to Boats for Sale, New and Used Boats and Yachts - YachtWorld.com
search for sail from 35-45 feet, pick a few at random and look at the pictures and descriptions. You really need someone to help you just to get the terminology correct. Maybe if you post your location someone nearby will offer to let you look around his or her boat.