A rain shell is worthwhile(as are fenders, and shoes and socks made out of something fast-drying), as is some lightweight warm gear-- the record low for May in Minneapolis is 18F, and the average low is 49F, so the first few nights have the potential to be cold. At least bring some poly long johns, and maybe a down shell to wear under your raincoat while camping. You'll also likely hit some summer thunderstorms.

Here's a $400 BD bike that'd be suitable, although not optimal, for touring:
http://www.bikesdirect.com/products/...liberty_cx.htm