Have you thought about going with a 240SX? You can pick one of those up for a fraction of the cost of a 370, E46, or BRZ. I would keep the costs of your first car as low as possible, just in case.. Not to mention, the 240 is a great car for street or track, AND theres a ton of aftermarket stuff you can get, install yourself, and learn a ton about working on them at the same time. (insurance is WAY cheaper too)
Heres a great example of what you can get for half of what you are looking to spend.
1995 Nissan 240sx SE