Of course, a huge part of this equation is how much you want to spend. Have you talked to a lender? Maybe you are paying cash...? Are you okay with being outside of the perimeter?
There are many factors that need to be clarified before this question can fully be answered.
If you want to talk more in depth about your options, feel free to call
What type of investment are you looking for? If you want to create a portfolio of rental property there is a wide array of areas that attract a strong rental market. Likewise, there are alternate areas with strong sales of renovation resales. The key in either is to know what type of property and finishes the market is looking for. Otherwise you can end up with an unmarketable property.
Also, for the past 25 or so years, SW Atlanta has been the ghetto. Before that, it was filled with many blue-collar workers, so there are still remnants of the good old days with lots of plumbing, car mechanics (and factories) etc.
Also, most cities tend to grow (directionally) to the NE, so the SW is the complete opposite. Doesn't mean there aren't deals to be made, but the growth is probably not going to be as great as it would be elsewhere. Also, you're starting to get into the Clayton County side of things, which most Financial Advisors would tell you to not invest in two areas; Atlanta water and Clayton County. I don't know if these are Clayton or not, and if not, they're probably Fulton, which south Fulton is not a great area for schools or crime.
What is your estimate of Cheap?? For some this could be $200K for others it could be under $100K.
What kind of investment? Are you looking for a renovation flip or a long term rental investment.
These are questions you need to ask yourself to determine what areas to look in here. There are different markets all around the city.
If cheap is your primary criteria, then you are looking in nice high inventory zip codes, my friend.
How long do you want to hold a cheap property?
When do you seek your first purchase of a cheap property?
10 or 20 purchases right now, or one or two right now?
You doin' all cash?
Who is going to buy from you when you seek to sell?
Get your real estate on.