You'll need to win some of the online cars for this but you'll get those for completing 230 online races (you don't have to win, just finish.)
You can get the rest of the cars by completing the relevant races in the Basic, Advanced and Duel routes.
There are faint bars down the screen when you look at the World Explorer, these are the class dividers. Use these as a guide to where the remaining car awards are in each class.