Any GSM phone that operates on the correct frequencies and is unlocked will work. In practice that means tri- or quad-band. Make sure that the specific phone you buy is configured correctly - I had a phone I bought in England that was tri-band and worked everywhere I go, but it was damaged by water so when I was back in England I bought an identical phone. Only when I got back to Belize did I discover that although it looked identical and had the same model number, this one was dual-band and won't work here.
You can buy a local Digicell SIM card at a number of places. Perhaps the most obvious is the BTL office just north of town.
On choice of phone - there are some models which take two SIM cards at the same time, although they don't all work the same way. You might find this convenient - I didn't bother.