Some people use trash bags for bedding, clothing and whatnot. If you plan to do this, I strongly recommend that you use the large clear leaf bags so you can see the bags' contents. I used regular Hefty bags for a two-block move many years ago, and all my towels and washclothes wound up in the trash by mistake. I think you'll find that large, clear trash bags are useful to have on hand even if you don't plan to use them for packing. When a box is packed, move it to the staging area, so you won't be tripping over it later.
Heavy boxes go on the bottom, lighter boxes and breakables on top.
I've found that it's safe to stack boxes about 5 feet high, if they're tightly stacked. If you plan to move during the wintertime, include a box of salt, in case the sidewalks are icy at either end of your move. As you pack, set aside a couple of boxes for things you no longer need or love. Donate them to Goodwill or another charity. In doing this, you've done a good deed, and made your move a little easier.