Disney/International Dr are good choices if the family is with you, might even be better if they're not!
The miles to the track aren't that bad since most of the trip will be on toll roads, 417, 528, 408.
What ever you do, stay off I-4.
My favorite way from south Orlando or Kissimmee to the track, head east on SR528, exit Dallas Bv, then north to SR520, then west to SR50 and the track.