Wild camping can be found in Manistee, Huron, or Hiawatha Ntl Forests. All within a few hours of your town. Also, search the trip reports section. A lot of folks have done the trails in the northern part of the state.
You can probably find a vendor here on the board that will sell you silnylon to make a tarp. Look in the DIY section.
Have fun...and Welcome to the board!!