Along with what outlaw was saying - go autocross if you have zero real world (performance) driving experience. Preferably a beginner/novice school for first event. The lower speeds, tight corners and different elements (slalom, chicago boxes, etc) make it a great learning tool. If you have the money I'd spring for track days too, obviously. At least a couple of events so you get used to what it feels like to REALLY push a car. The more the better though. If you can do this in a 370Z, great, if not - don't worry. Any well balanced front engine/rear wheel drive car handles about the same as long as the owner hasn't ruined it with terrible coilovers/spring rates. I've driven Miata's/BRZ's/370z and no ****, they all feel mostly the same. Sure their dimensions are different, the Z is much heavier than a Miata, but has more power, etc but you'll still get the overall same feel. I just co-drove a friends BRZ this past weekend and threw him $20 for tires/gas. Not even a $100 weekend after entry fee, food and what not. Can't beat that. Once you're used to driving fast, one of the best things I can stress learning is: Not overdriving. I did it at Silverstone, I still do it now even though I know better. Beat that through your skull and you'll go far.
On the fitness front, it's not hard to be in good shape for GT Academy standards. A basic PT regimen should be plenty pending on the condition of fellow contestants. Some running, pushups, situps, etc multiple times per week similar to military standards. Want to go a little beyond that, something like p90x should help. Want to go full on beastmode, join a crossfit box (been doing it almost 6 months now and me now could kick the **** out of me from GTA2012). Of course, some of this is dependent on where you're starting from. If you're coming from the couch and thinking fitness could actually be a factor in elimination, I'd start figuring out how to go beastmode stat. It's just one less thing to worry about if you're in better than average shape and can eliminate that as a factor.
. Now I can officially be not fast enough eh 
. Here I'm lucky to be able to do 30 jumping lunges and you're doing 70??? Agh, that's impressive. I won't even touch on the hand stand push-ups... impressive stuff, sir 👍
If you want to be the best, you gotta beat the best......Kinda like me David, the Aliens Goliath. 
), so I knew it required sorting. Didn't think of the initial list being wrong. 
