^^ Crikey, a sensible post
Could maybe look at a drift day? The 'sidewaysness' of it feels like you are ragging the shit out of the car / a bit out of control, when in fact you might be going fairly slowly, so it's much kinder on the brakes (which you will most likely need to upgrade on any car before you take it on a track day).
You don't need anything other than a lid for track / drift days, and no special license (normal road license is all you need).
It sort of depends what you want from the car, but I would highly recommend a MK1 MX-5 for a track car. Yes, they are 'hairdressers cars', they aren't quick in a straight line (but pretty much nothing feels fast in a straight line once you are on track, unless it is absolutely ballistic, like 350bhp/ton+), but they are super reliable, cheap (to buy and run), and spares are plentiful. Old 106s and Saxos are pretty good too, but you can't take one on a drift day
I fell into the trap of thinking I needed a 'fast' car for track days, but it's all about cornering speed, and the satisfaction of sticking with / passing something that's got twice the bhp is mega!