They let you accelerate, brake and corner at far higher speeds than stock. Tires are definitely the first upgrade you should get. Up next should be a racing muffler and performance chip. Both yield a great power boost for relatively little cash, and if it's a turbo car, a racing intercooler also delivers an impressive increase in power, again for a relatively small sum of money. Then it's just a case of personal preference and how much money you have.
Suspension definitely helps, as does a racing transmission and other engine goodies.
Lightening the car also gives a great performance boost, and finally a stage turbo or NA tune to boost the power through the roof. We didn't lose one single manufacturer race using this strategy. Well, let us tell you. You earn 50,000 credits for winning the race, but the best thing is that the prize car is a Speed 12, which you can sell for cool 500,000 credits. Since the race takes about five and a half minutes to run, you can basically earn yourself in excess of 10,000,000 credits an hour, as long as you don't lose.