My immediate thought was C63 but might be too much on the budget. The power is about right at around 450BHP though.
I think anything E might be a bit too heavy for a track car personally.
I once had an E36 M3 Evo and out the box, the E55K is nothing like in the same league so you would have to do a fair whack to it. It does handle well for what it is, but being 1845kg you will get through some consumables!
I would personally buy a Caterham for the track and another car that meets the other requirements.
This might not work for you though given your budget and there are storage considerations of course.
If it had to be a single car, I'd stretch the budget with a loan and get this as at least you know it will be sorted and a minter coming from Jay:
https://www.mercland.com/car.html?id=5351
After a few days hunting around I think I’ll keep hold of the M3. I have a Forester 2.5XT which was going to be swapped for an electric ‘town’ car; hence needing a bigger second car. For now I’ll keep the current rolling stock and save up a few pennies for a C63.
Thank you all for the help.