I have a thick felt boxy basket thing I just stack them in, and a mini spray bottle from the dollar store that also fits in said box. I got it from Walmart in the home organization section. Three (small, medium, large) nested together for like $10 I think (clearance). I use the small one for wipes and the other two in drawers to help keep baby clothes organized.
Re: Cloth Wipe Container
ETA: it's basically this with a metal gromet on one side for a handle.
https://eurostyleyourlife.com/media/catalog/product/cache/1/image/9df78eab33525d08d6e5fb8d27136e95/0/3/0330032461_1.jpg
Like I said I figured I was over thinking it. I've got a little basket that I just hung up that I think will fit the wipes & spray bottle.