I need to sow grass on a large area under an oak tree. While I'm at it I
want to over seed my entire front lawn. My question is what seeds, if any,
are best for areas in both shaded areas and areas in full sun?

I know autumn is the best time for over seeding, but I don't want to wait
that long. So other than waiting for fall, when would be the second best
time for doing the job?

I live in North Central Texas which is in zone 8.

Thanks