The first thing to note is that most people think of Nassau as The Bahamas. Whereas in fact there are hundreds of islands, of which about 30 are inhabited. What you can get easily in Nassau you might not get at all on one of the other islands. Everything is expensive due to duty and shipping. On Abaco, the 3rd most populated, you can get pretty much all the basics plus a bit more. There arent many shops though, so little variety and no really high end stuff. There is now one furniture shop left, but the items are surprisingly okay for a small island.
The second thing to note is that everything brought into the islands, new OR old, is subject to duty of varying degrees, which is why it is expensive. It would be wise to check how much it will cost you to bring things with you.
I wouldnt bother with basics but definitely bring high quality items like bedlinens, towels etc if you value that sort of comfort. You can get household linens but they are fairly mediocre in quality.
Cafetieres. Cant get here. Books. Unless you use an e-reader. Very few books sold here, I dont know if Nassau is better, I dont remember seeing any. Any specialist electronics. There are random small places that sell electronics but nothing specialised. In fact all shops are small and random! Except the hardware stores and supermarket.
We ordered in a toaster oven as cookers here apparently dont have grills. This is so we can do things like cheese on toast.
So, you can come and live with just a suitcase, you can get all you technically 'need' to get by. Depends on what you want to surround yourself with.
