If I'm buying, shredded hardwood is the only thing I would buy. It can be hard to get started without buying an initial layer.
But for free, the possibilities are numerous, probably all already said. Some may be most appropriate in the back yard, or at least out of sight while still recognizable. Leaves, grass, shredded paper, general small shrub trimmings, kitchen scraps, rough compost, pulled weeds (that haven't made viable seeds yet), pine needles, etc.... I use what becomes available when it becomes available, or as soon as winter knocks some things down if plants are too tight at the time. I don't think of mulching as a "one and done" but an ongoing process.
