Buy a newer Corvette or other actual mid-range sports car that never seems to be used for "sports" (sports here usually means shitting up the chassis configuration/handling, overtuning, and pushing 250hp per liter in the vain hope that nothing fails catastrophically while you're driving like a exceptional individual on public roads).
The biggest problem is there's not a ton of options. You will spend a minimum of $20k, but for that you can get a minty-mint C6 LS2 Z51 garage queen with all the options with like 50k miles and all the OE parts still in good shape because a 70 year old man drove it below the speed limit. Add 5 grand or so and you can get a newer LS3 one. It's possible to find a mint "Z07" C6 Z06 with low miles for around $30k, but the wacky engine is notorious for needing certain preventative things. However, the Z06 may as well be a supercar the way it's equipped.
You can get clean Z's in this range, but they're more susceptible to street modders. Something like the Nismo 370 has a better chance of being factory mint because it was optioned to begin with, and rare. Later model M3 cars are pretty sick, but expensive to fix and the entry cost is higher too, starts to get kind of stupid. Porsches of the mid-2000s have fallen into the $20k range but as much as I like them, it's not a particularly "sensible" choice for those with limited resources. Include the Dodge Viper here, the first generation can be had in the $20's, and they're all pretty much garage queens. It's a bizarro supercar though, and while the engine might be cheap to fix, I dunno about the rest of the parts. The GTS second generation is still kind of expensive and also subject to supercar tax.
If you want a "sports" car that's actually just a muscle car, the Camaro/Firebird LS1 cars can still be found as unmodified garage queens, for closer to $10k. Newer gen RS and SS Camaros, and I assume the ZL1, were unreasonably expensive when I looked. The Mustang sucks, I'm sure there's a few specials in the family that are good (Roush mods, Cobras) but it sucks.
Oh, and if you're gonna make a project/modified car, buy one that someone's already killed their wallet on powering up. It'll still be beat to shit, and you might need to buy new performance parts anyway, but you'll get $50 grand in parts/labor for about the same price you'd spend on a mint factory version. There is almost zero return on performance modifications, and just the parts cost thousands upon thousands before you get to labor.
