There are lots of options out there. One of the nicer cars that I've run for that purpose / price range is the 240SX. I prefer the mk1 (pre 1991) models, but the later ones may appeal to you. It's a capable car that is confident around corners as well as high speeds. The rear seats are negligable, but so are the Supras. A 4 seater RWD hatchback is a lot to ask for in the 90s, as everyone chickened out and went FWD or coupe.
If you wanna get funky, you may consider a Porsche 928S. (1986+). The prices on these have plummetted and you can be sure that they were the previous owner's pride and joy (No beaters). Most of them are automatic, and the 5 speeds are reverse H patterned. A truly fun car to drive, that is SUPER confident at speeds. It's an honest 150mph car. And there is no questioning it's sexiness (You can get a slantnose for it, used with some repairable damage for about $500 complete). Avoid autos.
RX7's are lighter and flickable, lack the rear seats (Well, mostly) but are also quite capable at high speeds. the 2nd gens are nearly flawless (Except the low quality building materials). They are awesome handlers, and Wankels do more with a Turbo than you may have thought possible.
The Porsche 944 is much the same. Lacks rear seats, but is a complete barn stormer.
If you can get away from hatches and liftbacks, BMW offers very nice rides for that price range. I'm not a BMW fan, so I can't go indepth.
As far as the Mustang / Camaro thing, you can make those cars handle like they are on rails. You just have to be really careful of your choices for parts - Too much torque will make any car lose grip around any corner. The thinking man will put the Cobra DOHC V8 in a 1993 Fox body hatch. Lower it, Ford Motor Sports all the parts out and hvae a car that can conquer a road course. Same with the Camaro - Right suspension parts on that wide track (Again, thinking pre92) and you'll rock the casbah.
IF you can go FWD , then your options totally open up. Of course the smartest thing in a FWD is a honda swap. But if you need the kind of car that can do 120mph all day long without breaking a sweat, Lincoln Mk8s, Pontiac Turbo Grand PRix (1989 is the only year), Beretta GTZs or even a Corvette are coming down to your price range.
The possibilities are endless, if you think outside of the box and start to shop smarter and not with the trends. Supra values are dropping pretty badly, and you're catching the tail end of a high resale Supra year. You're going to take a hit on it and the prices of aftermarket gear won't come down at all.
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