Why do people insist on the 111r RM.
Man up and use the elise S1 '96 RM as it's better through the twisties.
Power is not everything.
I literaly just took your suggestion a few minutes ago and I dont regret any of it!, the '96 ELise RM feels so much more fluid and natural compared to its more modern brethen. a really enjoyable car.

Back to topic, the ten cars I would suggest are:
1: Isuzu 4200R - A well overlooked car, but has plenty of potential, sounds like no other car and feels pretty nice to drive, with quite a weighty feel as well.
2: Chaparral 2J - This car just screams epic, the speed of its cornering for such an old machine is staggering and it's looks are so unique, not even the X1 can match.
3: Mazda RX-8 LM Race Car - Ok, it may not be as powerful or as stylish as its older brother (the RX-7 LM Race Car) but its still a pretty good car in its own rght, and with a nostalgic paint job referencing the classic 787B, you know its going to be good to drive.
4: TVR Tamora - Seriously, good luck trying to tame this animal, it truly is not one for the faint hearted [exceptions being the Speed 12, for obvious reasons, because that is incomprehensibly insane] but for a good tail-kick around some corners, its really fun to play with, not a good racing car, but for having fun while it tries to kill you, cant go wrong with this convertible crazy car

.
5: Lotus Elise S1 RM '96 - Thanks to the person I quoted, i now adore this car, a car which I completly overlooked in favour of the Evora, but now treat it equally and realise that this is a genuinely fun race car, the 111R is better at speed, but speed means nothing when you can have fun at doing anything else [cornering, acceleration, drift etc] and the classic Elise feels so much better!
6: RE Amemiya FD3S RX-7 - A really good car that I was very suprised about, it handled fantastically with just the right amount of cornering grip whenever you need it, and it will let you know if you overdo the accelerator pedal, but the drifting is so sweet you wouldnt mind it anyway, you'd just keep on sliding, its that fun.
7: Gran Turismo PDI Racing Kart 100 - There is simply nothing else like this car... I mean go-kart. A unique feeling and great fun for any skill level.
8: Jaguar XJ13 Race Car - B-E-A-UTIFUL, thats all that needs to be said about its looks, and its driving performance matches perfectly, a really natural feeling and fluid driving dynamics for such a classic car really make this car a standout in the classic race cars of the era. Also, do NOT get rid of its original colour, anything else just ruins it

.
9: Citroën GTbyCitroën Road Car - One of the few modern cars that truly stand out in all the right positive points, a aggresive, flowy design matches a perfect balance between harmony and chaos, and its driving feel also seems to follow that philosiphy, with staggering top speed and very good grip. It is quite the performer.
10: Daihatsu MOVE SR-XX 4WD (Fully Tuned) - Just because i can

but in all seriousness, its a pretty fun car to drive, its grip is phenomenal and speed is quite decent. As stock it isnt too bad either.
Honourable Mentions
Mazda Furai Concept
Citroën GTbyCitroën Race Car
Chrysler Prowler
Jay Leno Tank Car
Peugeot 905 Race Car
Nissan Silvia (CSP311) '65
Tesla Roadster
Maza Autozam AZ-1
Lotus Evora
Acura DN-X / Honda DUALNOTE Concept
Triumph Spitfire 1500
Chevrolet SSR
Suzuki GSX-R/4
Cizeta V16T
Chevrolet Camaro LM Race Car
Chaparral 2D
Nissan R390 GT1 Road Car
Tommykiara ZZ-S
Tommykiara ZZ-II
Chevrolet Camaro IROC-Z Concept
Spyker C8 Laviolette
Dodge Viper SRT-10
Toyota 2000GT