At their arrival in Portugal (Lusitania) the Romans loved to live in the Algarve. Wealthy Romans mostly had a "Villa Rustica" and a "Villa Urbana" to make optimum use of the rural and the urban setting. Later on the "Villa by the Sea" also became popular.
The most important choice you need to make if you are looking for a property in The Algarve is; "Where and how you want to live?" Perhaps the advice of the Roman politician Cicero to Varro in "Ad Familiaris" can give you some help to get started; "If you have a house with a garden and a library, you have everything man needs".