What kind of shoes you get depend on what you want to do in them, and what kind of feet you have. I have wide, flat feet, plantar fasciitis, 2 differently bad knees, and I run.
My perfect sneaker is a Brooks Adrenaline GTS. That sneaker is probably terrible for your high arches, and wouldn't have the correct support for tennis or aerobics or basketball.
If you want to run, I highly suggest getting fitted at a running store. I don't know if other sports stores do sneaker fittings for other sports - maybe someone with more experience will chime in.
Good luck - sneakers are important!