First - you can't have one car do everything you mentioned. Drag racing is COMPLETELY the opposite of making a car turn left and right... So my #1 advice would be to figure out which part of the sport you're the most interested in and do that well...
Second - Once you figure out #1 - buy a used car (Fox body) on Racing Junk or somewhere else that's all set up for what you want to do. Used race stuff is relatively cheap compared to buying and building.
Third - You're going to need a lot more than just the "car"... don't forget about a trailer - something that can pull the trailer... tools... spares... tires... and a budget for breakage which is different than "upgrades/changes"
An example of "Third".... I have a couple race cars.... I've now rebuilt the motor in one of them 4 times in the last two years... and the upgrades to that car exceeded the cars original cost. Versus -- I just bought a track set up Miata for $5500.... and an aluminum open trailer for $5,000 --- this combo is light enough to be towed with a mini van I think (Laughing here). So for 10 grand a guy could have a dedicated track / autocross car... I'm confident you could find a Fox Body Mustang in that same price range.
Fourth - The heavier the car - the faster you'll go thru brakes and tires.... the more powerful the car - the more you'll break expensive parts. An example of this is my Lotus 2 Eleven has yet to chew up a set of Yokohama A001 Softs or a set of Brembo pads and rotors... versus my '65 Mustang which has gone thru (in the same time) a couple sets of Hoosiers... rotors.... pads... a Jerico transmission... a clutch... The Lotus weighs 1470 pounds... the Mustang weighs twice that.
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