Here are some ideas -
BMW M3 or M5 - older ones are withing your budget - a bit obvious but at least people will have heard of them when you get back to the 'States - There is a diesel 330D that can be madeas quick as an M3 with just a remap
Scooby Impretza turbo - again bit obvious but can be made VERY quick (400-600Hp in light car) with relative low cost - older ones are within you budget - the Mitsubusi EVO tends to be a bit more expensive but again, older ones may be within you budget
A lotus Espirit turbo is a good car to take round the "ring some are within your budget - a cheaper alternative to a Ferrari - some 70s/ 80s Ferarris may be withing your budget but of course you would need to grow the "magnum" mostashe if you got one of these!
You could get a Masarati biturbo - interesting car - slated in many quarters
The rear engined Porsches (911/ + derivatives) tend to hold their value - but some front -engined 944 or 928 are within budget - the 928 is a fast car (180+ mph)
Since this is a Ford forum i must mention the Mondeo mk3 ST220, not as fast as some of the cars mentioned and realatively difficult expensive to tune, but a grast handling car and will reach 150mph with a long enough bit of road, very good value and a lot of car for the money
The Focus ST225 can be made very quick with very little outlay, a remap alone brings it to 270Hp 400+Nm, and with a bit more work, 350Hp is withing reach without breaking the bank - this would be a serious alternative to an EVO or impretza turbo
If you know where to look there are quick cars that can be picked up for "peanuts" - big, thirsty cars are not that popular as seconhand buys, with the price of petrol over here
There was a car called the Lotus Carlton that was the fastest production saloon at the time (early 90s) a rare classic now, but they could be picked up surprisingly cheaply
There are some quirky cars that could be cheap to pick up over here that would be very rare in the States, There is a car called a Rover 827 Vitesse - although "on paper" it had a sluggish 7.4sec to 60 and a low 140Mph top speed, it can be hustled round a track surprisingly quickly, one held the saloon car lap record round the TT course for many years (record breaking 100mph lap- Tony Pond - 150mph+ inches from stone walls on some parts!) i can tell you at high speed the handling is much better than a Sierra or Escort - having owned one - the 2.7L v6 had a type of variable inlet geometery developed on F!cars, - so it had a very - wide/ lat power/ torque curve the engine was made by Honda and the NSX supercar engine was based on it
PS - if you are going to take a Fast 90s car "flat out" round the 'ring (or even the ST220) fit some bigger brakes 1st!
Of course these speeds would only be on the track - + the 'ring can be a dangerous place so be careful!