17's and 15's
There are lots of guys running 17s, or bigger, on the front, with 15s on the back. Best race tire selection is in 15s, the guys with big brakes might need to run 17s to clear the calipers.
With a nice tall tire in the back, it looks fine.
There are definitely decent race tires available in 17s that are drag radials. Hoosier, M/T, Nitto, and I think M&H, all make some, some better than others.
They are expensive, and won't last long on the street.