While sorting out the gear side of things, you should also research on routes and permits. You may already know that the Wall is disjointed / eroded in numerous sections. If you are thinking of wild camping along the way, that may be forbidden in many places as well.
I haven't done this, but I wonder about your west to east route. Curious, have you thought about doing this the other way around -- from east to west instead? The eastern terminus -- Shan Hai Guan -- is on the coast in Hebei province, a few hours' train and bus ride from Beijing. The Wall then winds its way through the north of Beijing towards Jia Yu Guan out in the west. Hate to say it, but the Beijing and eastern sections can be extremely crowded and touristy. For myself, I would hate to have that as my grand finale. Instead, I'd rather start with the crowded, developed, relatively polluted areas and work my way west -- hopefully with the scenery improving as I go -- instead of the other way around...
If you do go from east to west, you can take the train from Jia Yu Guan further west to Kashgar. The "spectrum of civilizations" changes ever-so-slowly from Han to Turkic as you move westward. Kashgar brings you to just tens of miles to the border with central Asia.
Anyway, food for thought.