There are many pistol storage boxes that are great cheap storage for chess pieces. This is one example on Amazon for 36 bucks. Each piece nestled individually in foam with no piece to piece contact, and no piece movement if you are carrying or moving the box, even roughly. I have some cheaper versions in black plastic that are usually 20 to 25 dollars.
All Purpose Zipper Bags from Walmart. $2.00 a bag is a cheap option. For storing I don't have a need for bulky padded boxes or cases. They are not going anywhere and these bags do save a lot of space in my closet.
https://www.walmart.com/ip/All-Purpose-Zipper-Bag/123067590?wmlspartner=wlpa&selectedSellerId=0&wl13=3295&adid=22222222420449455996&wmlspartner=wmtlabs&wl0=&wl1=g&wl2=c&wl3=501107745824&wl4=pla-293946777986&wl5=9026562&wl6=&wl7=&wl8=&wl9=pla&wl10=8175035&wl11=local&wl12=123067590&wl13=3295&veh=sem_LIA&gclid=Cj0KCQjwl_SHBhCQARIsAFIFRVWtg5uGoZOl_2MyDncqfo_hLa1BY-oGnZE-gn_aK2Mt27xJqHzWR0AaApiSEALw_wcB&gclsrc=aw.ds