Michigan is also a "shall issue" CCW state, which means that if you don't have a history of criminal or mental problems they HAVE to issue a concealed carry permit. A Michigan CCW also allows you to carry a loaded hangun within easy access in your vehicle. You may NOT carry in any place that gets more than 50% of its business selling alcohol in open containers (e.g., bars), sports arenas, schools (though a parent with a CCW MAY have their gun on them if they are picking up or dropping off their kids, provided the armed parents stay within their vehicle), or movie theaters that have a capacity of over a certain number of people (I think it's 1500, but don't quote me on it).
In order to buy a handgun, you must first go to the local police, sheriff's, or state police post and get a "purchase permit" (which you have to fill out and have notarized). Then, when you buy the handgun, you take it back to the law enforcement agency that issued the purchase permit (you have 14 days to do so, I believe), and they do the so-called "safety inspection". Note that if you have a CCW, you don't have to get a purchase permit. There is a special form that you fill out at the seller's; you get one copy, the seller gets one copy, and the original copy gets sent to the state police in Lansing.
Michigan is also a "castle doctrine" state, which means that if you are attacked you are under no obligation to retreat if you are any place you have any business being in the first place, and may use whatever force necessary within reason (up to and including deadly force, if necessary to preserve life and limb) to stop the attack.
Black powder handguns are considered "antiques" and do not require a purchase permit. However, cartridge firing handguns that are classified a s"antiques" under federal law (1898 or older, in other words), DO require a purchase permit if ammunition is still being made for it.