Help me plan my trip to Nashville?

We always wanted to go to Nashville and on a recent drive back from Georgia to Minnesota we stopped in. We didnt have time to see much. We walked by (but didnt get to go into) World Famous Tootsies and Hard Rock Cafe and The Country music Hall of fame. We also stopped in a bar and heard an awesome band play… but we only had a couple hours so we hardly got to see anything. Well this summer we plan to take a weekend and fly there early in the morning. So this is what I need for help. How far is the airport from downtown Nashville? Is it within walking distance? Is there a shuttle? Would we have to rent a car? And where is the best place to stay? We want something cheap but not a roach motel. And what are the top places we should have on our “To See” list? Also, if you name a hot spot we should see also tell me how much it will cost. Im trying to keep a low budget. Plus what would be an awesome souvenir to pick up while we are there? Thanks!