STT or STX need apt and car and advice

My fiance and I are looking to move to either St Thomas or St Croix from Mid May till the end of August.
Was wondering what was out there. I have been to St. Thomas a few times and loved the island. I am not familiar with St. Croix but only have heard good things. Any and all info would be great
for the Apt. we are looking for something in the 500$-1000$ price range
As for a car.. would it make more sense to rent one or to buy one and then sell it? Im not looking for a very fancy car just one that runs and has no problems and can get me from point a to b.
Thanks
Morgan