Originally posted by Docrwm and quick shirt.
And also Quick Shift. Although, shirts are awesome, too.
But yea, the DA 55-300 or even the 50-200 (not as long, not as popular) offer plenty of bang for buck and are relatively cheap on the used market, and even as new. But if you already have a tele lens, use that one.
AF settings, I am not sure how accurate AF-C is on that camera. Best advice I can give you is to try the different AF modes. You can also just use a narrow aperture (f8-f16) for a wide DoF and then manually focus ahead of time, if you know where the subjects will drive.
Panning is also a great skill for this type of photos. The trick is to keep the camera steady and follow the subject before you press the shutter and well after the shutter closes. And burst mode is your friend (take plenty of photos, then just delete blurry and OoF ones)