Running shoes have no side-to-side stability that is helpful if you are doing aerobics. However, my ankles are fine and I don't too crazy side-to-side motion that often, so I buy running shoes. I make the store people help me pick them out. Personally I like "a flexible shoe with some arch support".
I would suggest just going to the store (Sports Authority is fine) and asking an experienced sales person (i.e. not the 16 year olds they hired for the summer) what kind of shoe to suggest for what you will be doing.
"I don't know! I don't know why I did it, I don't know why I enjoyed it, and I don't know why I'll do it again!" -BART SIMPSON