For a light weight, iron sighted, factory ammo available, easy on recoil, under 75 yards deer gun, I'd suggest looking at an 8" barreled 357 mag - all you'll need.
I vote for this to best meet your criteria. You can always go bigger later. No one stops at just 1 barrel for a Contender. LOL.
"Therefore go and make disciples of all nations,... " Matthew 28:19
Handgun hunter since 1979 - haven't used a rifle since! HHI member #992, NRA, SCI.
