Savage, Stevens or Marlin to get a quality rifle while keeping the cost down.
I would not get the 770, there are cheap guns and then there are cheaply made guns. Not that it won't work, but it won't last well and you're better of spending $50 more and getting a better value.
Or get a muzzleloader and save even more.
If you certainly won't be shooting over 100yds, you can make the shotgun work.