When people say that they are interested in Greer, it usually takes a few more questions to settle in on exactly what they are talking about. There are the city limits of Greer, which have managed to expand via annexation over the past few years despite South Carolina's restrictive laws. It is strange looking animal, with lots of property not annexed virtually surrounded by areas that have been annexed. There is the downtown area, which is split by the Greenville / Spartanburg county line and which is undergoing a revival of sorts. There are the zip codes for Greer (29650 and 29651) which encompass most of the city of Greer plus lots of areas that are not in the Greer city limits. Then there are areas that are actually in Taylors or Duncan or Campobello or lots of other locations that people call Greer.
In general, the areas in 29650 that are not in the Greer City limits are really Greenville suburbs. They include some of the best schools and nicest subdivisions around Greenville. This area is often called "the Eastside" - meaning east of Greenville (and south of Greer). The more rural areas are likely to be in 29651, which is mostly north of Greer.
As for house rentals, you'll probably need to find a realtor who can find you rentals with an option to buy. This is one
property service with some houses for rent. Here's
another. And
another (http://coldwellbankercaine.com/search_results.php?dosearch=1&source=greenville&ar ea=&property_type=lease&subdivision=&street=&min_p rice=10000&max_price=&bedrooms=&bathrooms=&county= - broken link).