There are so many great options out there to keep it all together. My biggest suggestion, keep it all in the same place, and if possible, close to the garage. Mine is in my laundry/mud room area. It has come in very useful many times when we need to do a quick wrap before heading out the door.
I keep my wrapping paper, gift bags, and tissue paper (minus anything Christmas), in a container similar to this one from The Container Store. In the same room, I have a small container for bows and ribbons.
My Grandma has taught me well, and I keep every gift bag that is still in good condition (why not?). I don't go as far as she does and save all of the tissue paper. I find that it is usually to tattered to re-use, but if you have a delicate gift opener, go for it.