Hi Christine,
Yes you can buy a property on Antigua, we did without any problems.
We have just put our house on the market so are going through the reverse process.
Regarding buying a house you need to consider location, while a house by the beach or in a low lying area might sound attractive when the bad weather or god forbid a hurricane hits you do not want to be near the sea, besides the island is only 10miles x 14miles so you are never far from the sea, also living higher up its a lot cooler.
We bought a house that was 13 years old and had survived earth quakes and hurricanes unscathed. Unfortunately the build quality of some of the newer properties is questionable and haven't been put to the test.
When you find a property you like the real estate agent will request a deposit that he will hold onto while you engage a lawyer who will submit the required forms for land ownership and property ownership along with a request for temporary residency.
This is normally a formality unless you have a criminal record but can take a VERY long time. Should the government reject your application then the real estate agent would return your deposit.
Once all the paperwork is completed you make your final payment via your lawyer and the process is complete.