A few ideas that come to mind. First, I wouldn't spend the whole amount on the car, rather half on the car and other half on aftermarket parts to maximize performance and safety.
The Miata is going to be one of the best bang for buck autocross vehicles you can find. Personally I can't get past the looks so I wouldn't buy one but to each his own.
Here is a short list of vehicles I would consider if I was in your shoes. In no particular order
1st gen Nova W/TCI's Pro Touring Front and rear