the answer is miata
nothing is going to be as connected to the road, easy to fix, and reliable under 10 grand as a Miata.
Although high mileage 350z's are available sub-10k, just realize you are getting a high mileage car at the border of your budget.
but seriously Miata- you can get a mint NA for 4 grand. Depends on what you plan on doing, but for minimal $$ you can tweak it as you see fit, and at the end of the day you'll actually have money left over to take it to the track.
the motor is a joke to work on, all of the drivetrain components can be easily accessed, etc. Learn to drive well, work on it, and then sell it when you are ready to upgrade.