The 996 911 is always a rewarding car. Great handling and braking but a little under powered (around 190- 200rwkw for an early C2) compared to our usual lightly modified skylines. Not that an average driver would complain about it on the race track but, under powered nevertheless for its status as the iconic performance car. Exceptions are the Turbo models and GT variants, which I assume would be out your price range even for an used example.
A Boxster S would still be a better car than the Z4 coupe in terms of both handling and performance, unless we are talking about the Z4 M coupe. However, a Cayman S is always more special and a better all-rounder.
I would not recommend a RS6 if you are after a performance car. The previous generation RS6 was too heavy and was only fast in a straight line. An E39 BMW M5 would be a better choice assuming you want a family car that is also capable on the race track.
The E46 BMW M3 is the pick of the bunch in my opinion. Great all round car, comfortable enough for daily usage and is a proven weapon on the race track. If you do intend to track the car, make sure you upgrade the single piston brakes as its the only area of weakness for the M3. Again might be slightly underpowered for your liking but the glorious sound track of the engine more than enough makes up for it.
Cheers