Well, reading through the posts my money would be on
1. R spec tyres on lightweight rims - cheapest performance upgrade you can buy.
2. Upgraded brake pads
3. Probably suspension - you need to get it stable through the braking area, should allow slightly more corner speed and not bounce around as much
4. LSD: read all the posts, everyones spinning wheels coming out of corners, its a very slow way around a race track.I think if you fitted this and all of the above you'd be lapping faster than the upgraded power cars without any chassis work.
4. Power upgrade: By this time you'll be a red hot confident racer (we can dream) and can actually use the extra power as you'll have a chassis begging for more oomph.
Just my thoughts, but above all guys be a little careful and do a professional driving course.