Some areas have type 3 whitetail tags and LQ or general tags.
In years past there were usually left over whitetail tags but they have been getting pretty scarce in the leftover draw.
I would apply first choice as a type 3 tag if that's the one you want.
With price increase this year I think not many leftovers will be available, many are burning PP and getting out of Wyo hunting.
Black Hills have general deer season in Nov. open to mule deer and whitetails.