I’ve been doing something like this for a while. Four zipties poked through a 20x20 furnace filter attached to a box fan. Price is effectively one air filter (whatever quality you want) and some zipties. Already have plenty of fans sitting around, but they’re still cheaper than pretty much any filtration system, and seem to work far better!

Just be aware that the stronger the filters you use, the faster the fan motor will die trying to pull air through the filters. Probably still cheaper than buying a hepa filter, but you would need to replace the fan every few months, or go for a lower power filter.