A little late perhaps, but I'd like to echo the comments of a few of the posters who know what it means to take a car on track without an unlimited budget.
Top priority is something light. Primarily because the weight is your enemy on track. Most performance road cars feel like heavy wallowy tanks on a circuit. I've raced an assortment of cars from single seaters, prototypes and road derived cars. The bigger heavier cars, even when fully stripped and race prepared (eg M3, Evo, Mustang etc) are never as much fun to drive as lighter cars like an Elise or an Atom.
Not only that, but the cost of running a heavier car is dramatically higher too. Tyres, brakes and fuel alone will be more than double the cost you'd see on a lightweight car. For example it may surprise you, but to run a single seater like a formula ford for a day on track generally will cost the same or less than something like an Elise, and significantly less than say an M3.
My recommendation would be the Atom. I raced one in the Atom Cup series for 2 years and what always impressed me was that I could go testing, do well over 100 laps in a day and the car would just work and feel as fresh at the end of the day as at the start. In 4k racing miles I don't think we changed the brake pads, tyres lasted for many 100s of laps and it wasn't even that thirsty. Not only that but it was the only road car I have driven that matched a single seater for the entertainment value. They are genuinely quick and very lively. It took an exceptionally good driver to get the most out of them so it will always challenge you.
They were a little flawed as a race car as the lack of
anti roll bars meant we ran the damping too stiff to compensate, but if you aren't chasing the last few tenths of laptime, more sensible damper settings resulted in a hugely fun but forgiving car.
If the Atom is a little too raw, then something along the lines of an Elise or Exige would be worth considering. I see that the exige is high on the list of options - the only thing I would say is that performance doesn't necessarily equate to more fun. Feeling like you are driving an Elise at near its limits could be more enjoyable than feeling like you are only scratching the surface of the potential of an exige, that will have a lot more grip, be less forgiving and will be harder to reach the limits of. What you enjoy more will depend a lot on your own personality. Incidentally, I think an Exige is a decent choice, but I think it's just worth questioning what you want to get out of it before committing.
Have you considered getting a proper racing car? Something like a Formula Ford 2000 or Sports 2000 are in a totally different league in terms of performance and fun, but doesn't have to cost any more than regularly tracking something like an Exige.