The "limit" is your budget. If you don't limit your car choices to 4 and 6 cylinder models (Jap), you can go as fast as anyone ever has. On their best days, 4 or 6 do NOT "equal" 8. While there are plenty of pocket-rockets out there, they all have turbochargers or superchargers. For a fair comparison, you must use a supercharged or turbocharged V8. Once you put a power "adder" on a large V8, it is out of reach for anything less.
That being said, for a dedicated race car (one that NEVER dirves on the street), the best values today are among the GM "G-bodies". Those are the '78-'87 Grand Prix, Monte Carlo, Regal, Cutlass, Malibu, LeMans, and if you're REAL lucky, GrandAm (VERY rare).
These cars accept small block Chevy, big block Chevy and Pontiac V8s with ease (Olds too, but they aren't as good a choice). These are the three GM engine families of choice for a racer. The BBC is the most powerful and most expensive of the three. SBC is the most versatile and least expensive ("cheaper" is misleading, as there's nothing CHEAP about racing). The Pontiac is right between the two Chevys for power and cost. Plenty of good performance stuff out there today, unlike 10 years ago. If you like "big" torque at moderate RPMs, the Pontiac is the better choice.
The "Fox Body" Mustangs ('83-'91 or 2) are also VERY popular. The little Ford engines can be made to make enough power to have fun. The medium sized Fords are VERY good performers (351-400 CID range, small block). The BIG Fords are animals. The Fox body has a very good rear suspension for drag racing. It has become fashionable locally, to put small block Chevys in them. There are some rediculously fast ones with 422 or 434 CID small blocks. We have one guy with a 514 CID Lima (460-based) that is a MONSTER.
Another choice would be to watch sites like racejunk.com for good deals on cars already built, usually needing engines or other major drivetrain pieces. One can save a bunch by buying a car already built. Just make sure to take a person familiar with racers and racecars with you when you look at it. "Let the buyer beware".
Most important? Remember this is a HOBBY. Have fun and don't take yourself too seriously as a racer. If you're good, it will come out.
Jim