From looking at memphis craigslist 1 br apartments range from 300-$825 just from me scanning all those listings quickly. I also saw alot of 2br ones for like $500-$600. It probably depends largely on what its close to in the city. I would save up for at least 3 months of rent because sometimes landlords require a deposit of one months rent, and first and last months rent up front. If I were you i would drive around in the area of memphis that would be your ideal area to live, like close to your job or school or whatever, and look at apartment/condo prices in the area. You also have to factor in other costs that you might have to pay: electricity, heat (oil or electric), water, garbage... etc. You gotta check and see if these expenses are inclucded in the rent or not.

I'll be moving out in like 6 months when i transfer to a 4 year school. I cant wait to go apartment hunting... NOT! lol