The previous guys have covered the AR issue well.
From Michigan hunting regulations site:
Firearm, Crossbow and Bow and Arrow Rules
Shell Capacity for Shotguns and Centerfire Rifles
It is unlawful to hunt with a semi-automatic shotgun or semi-automatic rifle that can hold more than six shells in the barrel and magazine combined unless it is a .22 caliber rimfire. Fully automatic firearms are illegal. All shotguns used for migratory game birds (including woodcock) must be plugged so the total capacity of the shotgun does not exceed three shells.
. . .
Nov. 15-30 Firearm Deer Season
Muzzleloading Deer Seasons
During the December muzzleloading seasons, muzzleloading deer hunters can carry afield and use only a crossbow (except in the Upper Peninsula) or a muzzleloading rifle, a muzzleloading shotgun, or a black powder handgun loaded with black powder or a commercially manufactured black powder substitute. Only certified hunters with a disability may use a crossbow or a modified bow during the muzzleloading season in the Upper Peninsula.
All Firearm Deer Seasons - Rifle Zone
In the rifle zone, deer may be taken with handguns, rifles, crossbows, bows and arrows, shotguns and muzzleloading firearms including black powder handguns. It is legal to hunt deer in the rifle zone with any caliber of firearm except a .22 caliber or smaller rimfire (rifle or handgun). During the firearm deer seasons, a firearm deer hunter may carry afield a bow and arrow, crossbow and firearm....
All Firearm Deer Seasons - Shotgun Zone
In the shotgun zone, all hunters afield from Nov. 15-30, and all deer hunters in this zone during other deer seasons, must abide by the following firearm restrictions or use a crossbow or a bow and arrow. Legal firearms are as follows:
A shotgun may have a smooth or rifled barrel and may be of any gauge.
A muzzleloading rifle or black powder handgun must be loaded with black powder or a commercially manufactured black powder substitute.
A conventional (smokeless powder) handgun must be .35 caliber or larger and loaded with straight-walled cartridges and may be single- or multiple-shot but cannot exceed a maximum capacity of nine rounds in the barrel and magazine combined.
During the firearm deer seasons, a firearm deer hunter may carry afield a bow and arrow, crossbow and firearm. .....
Looks like the AR would be illegal or hard to make legal. Maybe you could find 5 rnd mags.
Personally, I would look for something like a bolt action 243 Win, 260 Rem, 308 Win, 338 Federal, 30'06, 270 Win or 280 Rem. My preference would be the 243 Win. Then get a good 6x or 3-9x scope.
Leupold 6x scope