My advice to anyone moving anywhere outside of their countries would be to store your belongings and move to your new area. Stay for 1 yr to see if you like it and if so, then decide what to bring etc.
Even US territories are vastly different than living in the US. Many people come to the VI, stay awhile and decide they don't like it after they have disposed of all their belongings. Living away from home is sometimes difficult for alot of people.
I wouldn't bring furniture to the VI. Some furniture would be harmed by the elements of salt air and humidity. I would see what I didn't need and bring only those things that I really cherish.
Cars: It all depends. The cost of shipping a car is around (approx) $1,500.00. Once here, they assess a import fee of 5% on the vehicle if it is made in the US. If the car is foreign, the import fee is higher. The roads aren't really all that good. Lots of ruts, potholes, sinkholes, etc and are rough on cars. I would not bring a car here. Purchase one here and a good, used car that is reliable.
I'm not aware of banned foodstuffs here, but bringing plants or food into the VI would have to be declared and Customs might make a decision on their entry based on the VI Dept of Agriculture rules and regulations. I know definately on plants, I'm not sure about food. Depends on what it might be.
When bringing anything to the VI, you must keep in mind that the climate is usually around 70-85 degrees all yr long. It's a tropical climate so light clothing is best. We have Hurricane season from June 1st to Nov. 30 each yr and you have to be aware and prepare.
Life is slower paced here so patience is a virtue!
We have sporadic electrical outtages, internet outtages occasionaly and some cell phone disruptions; however, I wouldn't trade it nor would I go back to the mainland.
I love it here. The climate, the people are wonderful, the ocean is always 80 degrees and life in general is 5,000% better than anywhere else I've been. I can't imagine anyone not loving it here.