I live quite a bit off the beaten path. I'm almost ashamed to admit it, but tar paper is a somewhat typical covering for small outbuildings around me. The tar paper does have to be redone every few years. The other would be T-111 (Texture 111) siding, which looks just like plywood with grooves routed into it so that it simulates old board and batton barn siding. This siding is cheap, and just gets painted or stained. There are wall shingles (called sidewall shingles) that were a popular choice for another generation. They were manufactured to simulate bricks, and lasted 20 -30 years. They are special order nowadays, and you wouldn't have very good luck with regular roof shingles. Vinyl siding is just about as cheap of an option as you can get now. Have you checked it out? You don't have to buy whole cases of the stuff at the home center, and you should be able to do a shed for peanuts.
"Nothing is foolproof to a sufficiently talented fool"