Brief overview
Hunters, as a general rule, have a lot of unique and somewhat difficult laws to deal with. Restrictions on what kind of sights a weapon can use for one, the shape of the bullet casing in others. Even the type of action can be restricted by state or federal laws.
Then again, some of us add our own restrictions just because we want to make I even harder on ourselves. We might be a tiny bit off our heads in some cases.
Anyway, I'm presenting 3 weapons suited to very different styles of hunting.
Stalking: a slow and methodical form of movement that relies on your senses more than anything. This is typically done with a very light rifle somewhere between 25 and 35 caliber, but my suggestion is a bit more unique
Tracking: a very focused and somewhat difficult way of hunting that demands skill and patience but can typically lead to a very short chance at a shot. This type of hunting is pretty popular in the Northeast US where large forests dominate the terrain
Special Season: unlike the other two ways I mentioned, this one can require very long shots in difficult terrain. In the Western US some areas have special seasons dedicated to muzzleloader hunting, they also have restrictions on the type of muzzleloader that you can use. In response to this, companies have started designing specialized rifles for this market
My suggestions are in the comments