Since GT1, I dreamed of it but never thought it was possible. Like you have to know someone in the inside. Have connections. Im taking auto mechanics this semester. Overall, I love driving, and I love cars. GT5 reignited my dream. Allthough I may never get close, is like a job that keeps me close to cars.
How about you? Already doing it? And if u wanted to go to the big boys, which would u want? NASCAR? F1? LE Mans?
Forget about connections, you need money. As long as you have heaps of cash at hand, you can find race drives pretty easily.
Money pays for the car, mechanics, transportation, etc. There are also several spec series which are open to pretty much anyone with the money to run, such as Formula Palmer Audi or the many car clubs and single-make championships.
You need connections if you don't have money...to find sponsors

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Anyway, I would be pretty happy racing in BTCC or lower. I don't have much hope of F1 or anything like that as I'm already 21 and lack the many years karting and single seater experience required. But sportscars and touring cars are pretty much open to anyone of any age.
One day I hope to at least enter into small club level events, such as historic touring car races. Doing a season of Formula Palmer Audi would be fantastic, even though I would get owned.
If I got to the point of running in historic touring cars or whatever and doing moderately well, I would then try to enter Le Mans. I don't think I could achieve anything greater than that in motorsport.
If I had £500,000 or so to spend on motorsport right now, I wouldn't spend it on actually racing though. I would spend it on testing to build up experience of driving fast on a track.