In reply to Lutefisk :
You are speaking my language. A cool car that will turn a few heads, you can work on it and learn, and do fun things with it.
The answer is GM malaise. Specifically, G-body. Monte Carlo, Malibu, Cutlass, Regal, El Camino, etc. There are three things you need to tackle on those cars to make them great on the street:
1) Power. With the exception of the super-expensive Grand National, they were all low-hundreds HP from super wheezy V6s and terrible V8s. The good news is that they (regardless of the badge on the hood) all direct descendants of all of the great V8s of the muscle car era. Muscle car V8s weren't as great as you think by today's standards, but every single one of them has amazing aftermarket support for as much power as your wallet can handle. Added bonus is that GM was consolidating manufacturing processes, so all G-body frames are essentially the same. Have a Cutlass car and a Buick motor? Drop it in. Have a Pontiac Grand Prix and a chevy 350? Yup, bolt it in. Want a 6.5TD in your Monte Carlo? Buy the mounts and bolt it in. Your G-body came with a THM200 trans and you want a 200-4r or a TH350? Already drilled. Have an automatic and want a T5 or T56? You guessed it.
2) rear axle. With the exception of the rare and expensive hi-power versions (GN, 442, etc) they all got the wimpy 7.5" rear axle. They're fine, but once you get over about 300-350 torque and sticky tires, they like to explode. There is no bolt-in swap (other than an expensive and rare 8.5" from the above hi-po versions) but again, aftermarket or some welding skills has you covered. Pro tip... a Ford 8.8" is a corporate ripoff of a GM 12-bolt and comes in Explorers and Rangers.
3) if you want it to handle well, front suspension. The fronts on these have really short spindles which makes a terrible camber curve. Again, you can dig into the GM parts bin and fix that or the aftermarket has you covered. If you're just drag racing every once in a while, leave it alone
Brakes are cake. $20 brackets on ebay will let you bolt on front discs and calipers from a last-gen Camaro. Hit up a junkyard for rear discs. Chassis parts from GM in those years are practically mix-n-match.
S10 is a close second if you want a truck. It's basically a G-body chassis with a pickup body. Obviously not that simple, but close.
B-body is also a good bet. Find yourself an Impala, Roadmaster, or Caprice and drop in whatever power you want. Caddy 500 is an easy swap, too. If you want really swanky, go D-body which is the longer B-body. Think Fleetwood, Olds 98, etc. Big, floaty, and heavy, but they already come with decent brakes and a much better front suspension. Two years ago I autocrossed an Impala SS at the challenge and we won CAM class (full disclosure... we were the only competitor in CAM class, but it's a WIN)
The best part in my opinion about the malaise GMs is that parts are stupid cheap. A reman alternator is $40. A brand new power steering pump is $50. Need a carb gasket? I have about 20 in a drawer in my garage. Water pumps are $20.
Another outlier (although I'm not a fan) is to find any Fox body Ford - Mustang, Fairmont, Thunderbird of a similar malaise 80s version. They are much like the G-body in that parts swapping is super simple.