Go to a bar or liquor store and ask for boxes. It helps if you go in thursday and say you can pick them up sunday.
A bar I managed threw out probably 50-60 heavy duty cardboard boxes every weekend. Breaking them down was a pain. Id happily save them for anyone who wanted em.
This is a great top - grocery stores will do it, too. Banana boxes are especially heavy duty, albeit with a hole in the bottom.
I'm dull enough to where I did the math on how many I could fit in my storage locker and opted to spend the $50 to have uniform boxes for maximum efficiency lol
It doesn't make sense to keep every box. I'd say be selective about witch boxes make the most sense to keep. Also, be selective about purchases in general and make a regular habit of purging. Refinement and balance will help lead a better lifestyle.
I have done this for our past two moves, and now that we own a house I keep them in our non-climate controlled cellar off our basement. My wife thought I was crazy until we moved and had good a good way to move a bunch of stuff.