If your budget is only 2k then it depends on how honest you are with yourself.
If you truly are just doing it for fun and wont instantly get frustrated that pals have much faster kit and leave you for dead then get a cheap hoon about. If they are all rocking M3's and similar 300bhp+ machinery round tracks like Donington or Silverstone then you are pretty soon gonna get ballache if you are competitive and wanna keep up to have the shared fun if in a 150bhp clio/golf/pug etc.
Last time I had a decent road car was the GT3 which wasn't that quick on road but was epic on track and immediately begs you to wring its neck, but there was a little thought (usually after taking off the helmet) that this is a 50k car waiting to enter the Stuttgart Cemetry backwards, in several bits !! lol
Its not a feeling I get in my track car which has probably also had the thick end of 50k invested in it over the years, but incrementally and therefore never makes you think "You gonna really suffer if you bin this" and as such its a more liberating experience. The fact that its considerably quicker than the porker probably also helps keep the mind focussed on driving rather than crashing !!! Only time I got sad was when I thought I was going to watch it burn to a crisp, but the marshals put it out quick and all was good after a day at the workshop with the guys, I'd have been a headless chicken if that was the GTR or GT3 !!
E36 M3 would be my weapon of choice for sub 5k trackfun
J.