With non-m bmw's it seems to be just better if you keep the revs below 6000. :/
It sounds like you want a 240. A friend of mine went though this. The BMW had power and was classy and nice, but a nicely built 240 is where he wanted to be.
I don't know how you can deal with the 330 and that open diff. With a price range of 20k you could get an E46 M3 and put it on coils and sways and be done. maybe some bushings. That's an engine which doesn't mind being used properly.