Shotguns dont suck for deer lol. Sure theres a little more kick, but theyre fine.
Remington 870 is a decent gun. Get one with 2 barrels. One rifled and one smooth bore.
I would say the only problem would be if youre gonna put a scope on it. Scopes are great for deer, but you would have to take it off everytime you wanted to go duck hunting etc. I dont see many bird hunters with scopes lol.
And for a bow, you could always do like me. I use multiple weapons. I have a bow for bow season, I use shotguns for firearm season, And a muzzleloader for muzzleloader season. Sometimes I use the Muzzleloader for firearm season though.
The ONLY thing I dont like about the 870 is I have had problems before when I would shoot a shotshell everything would jam up and I couldnt get it to unload because of being locked up.