Putting new shingles on detached garage. How important is tar paper?

I have a detached two car garage and live in Central Ohio. It has two layers of bad shingles on it. I'll be removing all of those. Before I install the 3 tab shingles, how important is the tar paper. Do I need it? 15 lb. or 30 lb? What purpose does it serve. Any idea how big of a dumpster I need for a 2-car garage, 2-layer shingle tear off? Thanks!