How much do you have to spend? Here's the basics of what you need (the costs are my estimates others may be able to provide better numbers):
1) A car - buy a car that's already prepped and has a log book or buy a car and prepare it yourself - cage, fire system, battery shutoff, tow hook, airbag removal, seat harness, window net. The list goes on for a long long time so be smart and buy a car that's ready to go. A cheap T2 or T3 car will probably be $10K+ and will not win but that's ok for now
2) Personal safety equipment - Helmet, fire suit, gloves, shoes, underwear, HANS device - $2K
3) Tow vehicle - You can't drive a race car to the track!!! $15K used $25K new
4) Trailer - open trailer will be $2K - enclosed $4K+
5) Tires - figure one set per weekend $800 - $1400
6) Tools - jack, jack stands, impact gun, etc. $1K
7) Race license - requires attendance at a school - $1K - $5k
8) Per Weekend costs - Brake pads, rotors every couple of weekend, oil change, tires - as above, hotels, fuel, meals, entry fees, etc. $1K - $2K
First year costs for 5 race weekends - $ 38K
Wow, that's expensive!!! And that does not include the cost of wrecking the car (your insurance won't cover it!).
I suggest you start with autocross and then try some track days. Much more budget friendly
PS. There are tons of young guys with good incomes who got into track events and racked up huge credit card debt. This stuff is addictive so start slow and don't get in over your head.
Alan Pozner