Actually i'm going into circuit racing !!!
you could start by enrolling yourself in a Track Day in your area to familiarize yourself with the circuit as well as getting to know your car better. a Nissan Micra or March as we call it in Asia is a good base. it is pure and handles pretty well. That hot little Nissan could prove to be an encouraging tool for your quest in circuit racing.
or better, look for advance driving courses or track day packages that provides coaching. An instructor in your car guides you through the 101s of circuit driving. mastering the ways of circuit driving may just mean that little advise from an instructor and that might just change the way you drive forever, for the better.
i took it as you're starting from scratch, but if your question is about getting into professional racing, with little budget, i suppose you could start collecting brownie points for that. Go for track days, make friends, get really serious about the sport, and then either get spotted to drive or form your own race team.
or if you have money and experience, simply decide on a race event you could afford to participate in, prepare the required car type, assemble a crew and start your career. and just invest more and more money maintaining your career, not knowing exactly the point but it seems to be worth it.
good luck and do update us