First, go to
www.vimovingcenter.com - lots of useful information there - so much so it will take weeks to read everything. There's also a very active forum there that has tens of thousands of threads that will answer all your questions plus hundreds more you haven't even though of yet.
Now, to answer your specific question: Yes, you can purchase a rental property in the USVI's and yes, you'd be wise to buy one with on-site management or you'll need to hire a local property manager. Now, most property owners will tell you that you probably won't be able to rent out your unit for the majority of the year unless you find a long term (say 1 year or longer) renter which then precludes you from using the property yourself. The really is more like 15 to 20 weeks rentals each year. Almost everyone I know who rents out their island homes just break even or lose a little on the rentals rather than make very much money. The income helps off-set carrying costs not fully cover them. Best to talk with your Tax advisor or CPA for more information how owning a vacation rental will affect your taxes.
One other thing to consider, if you buy a vacation home now and rent it out for the next 20 years what you'll have when you retire? You'll have a 20+ year old dwelling, that has had lots of wear & tear in a harsh tropical environment. Renters are notorious for abusing property that is not theirs. The sit on furniture with wet bathing suits, they run the a/c 24/7 even when they are "out", the sun & salt air play havoc with fabrics, appliances, paints and finishes. Expect to replace furniture, carpeting, appliances, upholstery, etc 2 to 3 times more often that you do "back home'.
Be careful before venturing into this type set up - do your research first hand, do not rely on promises of others or solely upon what you read on the internet.
You might be much better off, saving your hard earned money and doing some conservative "normal investments" to build your nest egg so you can purchase a newer or even brand new home when you are ready to retire.
Good luck following your dream.