Great idea. What's worked for me is simply taking a 20"x20"x1" filter and sliding it into the back cover of a standard $25 Lasko box fan. Cheap, easy option for air filtration in the home.
Vornado used to sell an air filter that took two 10x20” house filters. Before I discovered that model I was trying to build my own using computer case fans (my intent was to hide the loud box under furniture).
Home Depot used to carry those in the 1500 classification which was great, but those are getting harder to come by too, and even the regional chain that had them doesn’t as much anymore and I have to use the 1200 or once in a while the super basic ones. Or buy them from Amazon and fuck Amazon.
Air filters became a rent seeking gambit before the term rent seeking was even invented. We should just be able to use furnace filters. And speaking of furnace filters, if you have central air, do yourself a favor and change the filter religiously. Also helps slow down accumulation of dust in your ductwork, which makes it hard to ever get the house clean, though you can hire someone to come out and vacuum them out. They have something like a softer version of a chimney sweep’s brush with a longer handle. Last place we had them do that on like day 2 to avoid any problems from the previous owners.