There are many areas in the south side to consider, my favorite being South Shore. Great building stock, transportation lines, and lakefront. Not to mention Jackson Park, well established Hyde Park as a neighbor, South Shore Drive, and a thriving small business district.
As far as what to buy....
It's more a question of how to carry. If your buying a property which will serve as a primary residence, then buy what you want to live in and can afford.
Investments, whether single family or multi-unit, should be looked at in terms of carrying cost vs property income, factoring in reinvestment.
Feel free to contact me if you're looking for an agent. Otherwise, best of luck. You're shopping in a great area.