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On an almost related note, the fastest thing on 4 wheels I've ever squeezed myself into was a sylva stryker with a hyabusa engine and gearbox.
If you want to tinker in a shed and end up with a wicked motor, a bike engined kit car will cost at most 33% of that gt3, and will be considerably faster and more engaging.
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0-60 in 3 seconds for £3k is hard to beat.
and if you want the adrenaline hit
You twist the throttle.
I've never really driven any performance cars but I've chucked around a few "ordinary cars". Driving fast is a buzz. Twisting the throttle in second gear at 40mph on a 750cc bike however, is like "holy shit, how is this legal?"
Probably not a popular suggestion in this thread, but what about a motorbike? Cheap, easy to tinker on, unrivalled performance (for the money) and you can probably squeeze one in the garage. There's the new learning curve and if you want the adrenaline hit - track days my friend.