To see what the AI is using, there is a button before you go to join that particular race next to where it specifies tyre requirements and any other entry requirements, it is marked "Typical Opponents" and will show you power/weight/model of all the cars participating.
If youre just using a car for a single race though, dont go overboard on tuning, generally sports soft tyres and a gearbox is enough. Add wee bits as you go, and it will tell you what additions are worthwhile in the long run.
Like i said, gearbox and tyres nearly always suffice, but chucking a cheap clutch, flywheel, intake and catalytic converter is generally worth it as well for only about 3,000cr