My first thought was Cayman - You could probably get a lesser 911 in budget, but I think the Cayman is a better car.
Something like an F-Type would be great to drive, it's all degrees (I did a couple of laps around Longcross with a professional driver in a supercharged V6 and it's definitely NOT a slow car!) and you (like me, I suspect) may just find the front-engined, RWD setup more engaging and enjoyable - I certainly think, on the road, there's nothing to choose between good examples of each and somehow a front-engined car seems more naturally balanced to me, even if the physics says a mid-engined car should be better.
I have to say I always like the look of the Z4s with the retractable hardtops (no idea what E-number that is), although they always seemed to be rather disregarded by reviewers - That said, on the road, I suspect you'd be hard-pressed to find the limits without doing something really stupid.
Have you considered a Dodge Viper?
M