GM F-bodies (Firebird, Camaro) and the Corvette are good contenders as well. Barely counts but the C4 ZR1 Corvette (launched in 1989 for the 1990 model year) that made 375HP and was partially designed by Lotus would be up there as well. Taurus SHOs are quite popular now too. The Merkur XR4Ti was also a very cool car, and very cheap these days (mostly due to lack of parts availability without creativity); stock they only made a max of 175HP, but (speaking from experience) the fuel injected and intercooled versions of those engines can make over 300HP with little more than "turning up the boost." (The 2.3 turbo was also available in the Fox platform in the Thunderbird Turbo Coupe, Mustang Turbo GT and SVO, and a few others.)

Foxbodies are the most accessible especially when it comes to parts availability, community knowledge, and to a lesser extent these days, price. Except for maybe Fieros, and they have the benefit of being cheap too, for the most part. The GNX is absurdly expensive now, for what it is, but Cutlass Supremes and regular Regals aren't - they're popular conversion and modification targets.

And of course, there's the DeLorean. Probably the car with the single largest cult following. They're terrible cars - unreliable, slow, poorly built, but people love them.

If it were me and money were no object, I'd be going for the C4 ZR1. I've driven every other car mentioned above, except the GNX, and the standard TPI C4s making 250HP/LT1 C4s making 300HP are a lot of fun. I don't think you can get much more 80s America than a nearly 400HP Corvette with a top speed of over 180MPH. The Foxbodies are fun, but they definitely feel sketchy once you start making any more power than stock unless you spend a lot of money on suspension work.

Of course if it were really up to me there were no time constraints, I'd own a 1990s Buick Roadmaster with the same LT1 as the standard corvette and a T56 manual conversion (insert something witty about "faux wood that I grew up with"). But I already do, so that's kinda moot ;)