It's one at a time but what kind of championship is up to you. For instance I did a championship that they clearly wanted to be off-road but instead I did a super car championship. The game is highly flexible in keeping you excited and letting you race what you want instead of forcing you to race what you don't want to.
Right... I used the Ferrari for the first couple championships, even though the game clearly wanted me to buy a different car and try another series.