>>656210For a brush gun, a lever action in .30-30, .35 Remington, .45/70, or .444 Marlin will do nicely. Get a good peep sight and you're golden out to 125 or 150 yards if you practice with it a bit. A scoped .30-06, .270, or .308 will shoot further and flatter, but it's harder to get a good look at a moving target through a scope, so you have to pick your poison there.
Or you could do what I did, mount a scope high so you can see the irons underneath it on your .30-06. I've shot deer sighting both ways. Pic related.
Also, if you don't mind reloading (which you should do anyway, you'll get ammo that's better in your gun), you can get almost any milsurp bolt action and have a serviceable deer rifle. I have a MAS model 36 and took a deer with it a couple of years ago.