You will be competing with the 300 or so medical students living on Anguilla. They have taken up nearly all of the affordable housing because they can offer a landlord their tenancy of 19 or so months while they complete their first tow years of medical school. This makes finding a place more challenging for anyone else.
I know some expats who have managed to locate reasonable winter rentals -- but it has taken them YEARS to do so because they have established a network so that when something reasonable ($3000 US per month, excluding utilities) they jump on it in a heartbeat.
That is what we spend on our winter rental, but that includes intermittent cable tv service, no land line phone.