After beating Battle Machine, you will have the choice to pick either the Cobalt or the Civic. Choose the Civic. Go to your garage and switch the Nissan 240 to Drag Mode and the Civic to Grip Mode. Because the Civic was such a horrible Drag car, they put in a Stage 2 Engine along with other bonuses. You will still have these parts, so install them and watch your Power increase past Level 2. The Nissan will do way better in drags.
To make a long story short, Civics are better for grip, and 240's are better for drags, and both of em are available for free in the beginning.