Sounds like you have plenty of good advice here. I'll just add my quick comments, ignore what's already been covered...
What are your goals for getting into racing? Fun? Great, keep it simple and cheap and don't think you have to have the latest modifications and don't worry about what place you finish in. Your comment about getting to the "A" level before racing makes me think you would expect to be fast and run towards the front perhaps. I think most people get a rude awakening when they first get onto the track in a race. I know I did. If you allow yourself to get serious about it, better open up the bank account, it's gonna cost.
I started out in the "fun racer" category. Bought an old Yamaha SRX600 and basically raced it stock the first year, and had a huge grin on my face. I was just playing and didn't care how fast I went or what place I was in. But, slowly the fangs came out, I got more serious, the money started flowing into that old bike (which DID get faster, to the point it overwhelmed it's suspension and handling) and I collected a few trophies. That made me even more serious, and the first of two Honda RS125's came along. To make a long story short, it spiraled out of control, and I quit after 6 years. Too much money, and too many late late Sunday night drives back home and up to work on Monday morning with 3 hours of sleep. The fun started dissapearing and it became more like work.
But - I would not trade the experience for anything. I'm sure I'll remember the days of racing when I'm an old(er) man, and a smile will creep across my face.