There are ways to improve most things you talk about but traction will always be an issue in a front wheel drive car with ~300+BHP.
I was going to say geometry, but colesy beat me to it. The one thing I'll add is that when you start to alter it's geometry to improve one thing you can make it worse else where, so improving turn in with neg camber and/or toe can make it more unstable at higher speeds for example. There are examples of a 'fast road' setup on here somewhere, if I get time later on I'll take a look about.
You say you want something not common but all most people, ie non petrol heads, will see you in is another golf or audi - you'll be lucky if they know the mark or class let alone that it's a GTI/Ed30/RS3/whatever..
The RS3 is a really nice car, lovely sound and can be remapped to near 500BHP for £2.5k - which makes it tempting also.
Another car on my list is the BMW M2 - although, depending on the new A45, the BMW drivers reputation may sway me - plus they are starting to get targeted by thieves..
I love my Ed30, mine only has a stage 1 APR map so about 290-300HP roughly.. But during the winter, whilst it starts off fun, a few weeks in with it trying to kill me anywhere near full throttle in 3rd or less, 3rd is the main gear though, I'm starting to think about changing to something 4-wheel drive also. My gaze is on the MB A45-AMG, they are expensive but they totally destroy the golf in all weathers. I took one out on a test drive last summer, with my brother driving my Ed30 and I was really surprised how much faster it was. I'm waiting for the next generation to come out, sometime at the end of the year roughly/hopefully, to see what the new one is - even if I buy a used one at that point they will be much cheaper or I can deal with the salesman to get rid of 'old stock'.
Sometimes less is more, now the summer is getting closer traction will be less of an issue.
