As was mentioned, your best bet to save some money is for your buddy to bring the gun with him to Ohio and visit an FFL who will agree to do the transfer to you. It will cost you fees from the Ohio FFL, but you will save a lot of cash on shipping.
USPS prevents the handgun from being shipped postal. Private carrier (FedEx, UPS) will ship it, but they require expensive service levels (next day air shipment) to minimize their handling time... and also because they have gun shippers by the short & curlies and wish to profit on that situation.
Contact FFLs in Ohio before you plan the transfer. Your LARGE local gun store is often NOT a great place as they (often) turn up their nose at transfers when they'd rather sell guns. Large outdoorsy stores also don't want to use their FFL's for that purpose.
Small shops can go either way. Some are happy to get the small income from the service, others also feel like you should buy from them rather than from a private sale. Kitchen table type FFL's (and gun show only FFLs) are usually a good bet. You should be able to find a guy who will do the work for anywhere from $15 to $25. You might want to keep shopping if their price exceeds about $25, but use your own judgement. A nice guy that is accomodating, friendly and knowledgeable is worth $35 while an old curmudgeon who acts likes he doing you a favor and has a crappy attitude and mouth about the whole thing is not a good deal at $25.
While shopping for the FFL, mention that your friend will be bringing the handgun in with him, not shipping it.
You will be subject to a NICS check and a Federal 4473 form in order to legally obtain the handgun.
As far as Michigan is concerned, they do indeed register handguns. (it sucks) I'm not sure what needs to be done to "satisfy" Michigan requirements that the handgun is no longer "registered" to him once he's transferred it to the Ohio FFL, but if I were him, I would keep some kind of dated receipt with the FFL's contact information in the even that Michigan ever wants to bring it up.
I grew up in Michigan and the registration of handguns is a draconian bit of legislation that doesn't seem to fit the nature of the state. Most folks don't think of Michigan along the same lines as CA, MA, MD, NJ and IL, but the registration of handguns is a reminder of horsecrap legislation that should be repealed. I haven't lived there in more than 20 years, but I still have two handguns very near & dear to me that are "registered" to me in the state of Michigan.