Rifles can be used for deer in the U.P. and in part of the L.P. in Michigan. The shotgun and muzzleloader only areas are shown in the rule booklet available from the DNR and at license dealers, hardware stores etc.
The local library should have some books on hunting which should include info on dressing and butchering deer. If your doesn't you could get them through interlibrary loan.
Do you know anyone who hunts? If so, maybe they could take you out and show you the ropes.
I have seen some lousy gun handling in the deer woods. That shouldn't be, safety should be as much a part of hunting as of range shooting. Seeing a deer is an exciting experience, but you have to keep control of your muzzle and your emotions. Try and find an area where a hill will stop your bullet after it exits the deer. I use a .250 Savage, a much lighter round than your Mosin uses, and have still shot right through most of the deer I killed.
When I started out I used to find an area where there were lots of deer trails. If two crossed there I figured that was an even better place. Then I'd sit and watch the trail. Later, I found it hard to sit for as long as I could when a kid. I snuck around the woods for quite a few years. Now, I'm older and in poor shape so I watch trails again, usually from a blind.