Ohio is over run with deer. It needs a three day, multiple tag season.
Regarding the OP and the inexpensive gun, I use an old smooth bore Ithaca 12-gauge that has hung on the wall of the summer kitchen for four generations. It works just fine. I don't think I ever killed a deer more than 50-yards from the muzzle - I never needed to and I'm closing in on 35 years.