Ultralight style backpacks can fit to a luggage rack but you need to strap them on firmly and possibly add some width to the rack with thin plywood or correx. Larger backpacks may be too big and are better handled in a trailer.
You can just load up the back but it makes the bike a bit "tippy", esp up steep hills. You can distribute the load within your bag so the heavy stuff is nearest the front.
I met a guy doing low budget touring on a discount store MTB with a military kit bag strapped to the rear rack. Its not ideal but he was out touring and having fun.