PCSing to remote area - housing?

We're PCSing to a state without a base - Michigan.  We plan on buying a house but aren't able to go there beforehand to check it out so we'll have at least a month of trying to figure out where to stay.  What can we do/where can we live while waiting for our house to close?  Staying in a hotel would cost a TON for that long and there is temporary military housing or any of that in the area.  Any ideas?

Also, what is the cheapest way to do a full DITY?  And how do we figure out what the USAF will give us to do the DITY?  We're going to need storage until we get into a house, which puts Uhaul well into the $2K range.  We have 2 cars, one we could ship or tow, but we plan on taking a week of leave en route then 3 days of driving.