the hardest part in the classic playtrough is the race..so here are my tips
1. the first turn is probably the most important.
2. make use of the grass at the turn 3 and 4,
3. If the car goes in uncontrollable drift at one turn try and push the "ram" button (on ps that's "X")
4. if you manage on the first lap to place yourself on third position, there are some chances that the second place will have an accident on second lap and the first place on the third lap...like it did for me.
5. If you manage to secure the third position or better in the first lap ...don't rush.