Having run MY02 and 06 STI's on the track and in The Classic and Dutton Rallies, my 2 bob's worth is:
1. Pads - Ferodo DS2500 or Pagid yellow with DBA 5000 rotors
2. Standard radiator is fine if in good nick but keep an eye on the join of the top tank
3. Oil cooler not really required
4. Rims - get another set of 17's for track use or use the standard STI 17's for track and put 18's for street. Keep the offset +45 or more.
5. Tyres - you can run 235/17 R Specs on the standard STI rims and suspension without any issues but you may need to check for rear rubbing if you buy coilovers.
6. Fuel surge: Yes this is a problem after right hand bends on 1/2 tank or less so get hold of an STI in tank mini surge pot (or copy).

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