Michigan has some great hunting, but its crowded. Finding access to private land can be tough, but can be done. There is an abundance of public hunting land, and as stated, some gets hit hard, some hardly at all. Once you settle in, make contact with your county Conservation Officers, they can often point you towards under utilized public land with good hunting.
AS far as traditional archery opportunites, they are many. I strongly recommend you join Michigan Bow Hunters, our state organization, as well as Michigan Longbow Association and Mich Traditional Bowhunters. all 3 organizations are fantastic, and each hosts a weekend shoot/campout every summer, as well as other outings and banquets.
Most counties have local archery clubs, and while they are not trad specific, many have trad leagues. Michigan Bow Hunters affiliate club program is a great source of info, as well as published shoot schedules.