EDIT - the post below is talking about the Dream Car Championship...my bad.
To beat the World Championship I just used a Ford GT with race mediums, and it was insanely easy.
This actually depends on the field that they line you up with. I ended up with a full on Jaguar Prototype. He was probably 20s+ faster than the rest of the field over the course of the race. I had a fully modded Ford GT w/ 800+hp. I had to run consecutive 7:10's at Nurburgring 24h config and then 1:37-flat for 10 laps at Tokyo to edge him out. Also, impossible to win on Indy - I had to go back and get this again. Every race was a bit of work.
My ZR-1 RM would have done the trick a little easier. Although I had already defeated most of those cars with a stock Ford GT w/ racing mediums in Gran Turismo All Stars, it was just that 1 Jag.