As a former formula car racer, start with performance driving school and then SCCA schools and events.
Autocross is a great and affordable way to get into racing. You will learn car control and how survive nomex suits in 35°C weather. :)
Discussion
Also ignore the idiots who say women cannot do it. Read up on Danica Patrick and Sabine Schmitz, too. They are amazing. Fuck the haters.