I see a lot of people sharing recommendations for making this kind of DIY air filtration system. Since I have been using one of these for several years now, I have some practical comments and caveats:
Their useful lifespan is relatively short. A set of filters is good for maybe 60 to 90 days before it becomes so soiled as to be counterproductive, probably less if you have furry pets.
What the filters pull out of the air is deposited on their surface. You'll want to be careful not to touch the filters and keep kids and pets away from them. If possible, you should also put the unit on some stand or surface you can easily clean.
Removing and replacing the filters is nasty. The outer layers of the filters get filthy, and removing the filters involves using a utility knife to slash the tape holding the thing together, which will dislodge big clouds of crap. This needs to be done outside if at all possible. You'll want to wear a respirator and disposable gloves, and old clothes you can immediately launder (or bag and dispose).
You'll need to clean the box fan itself when changing filters. You'll want a can of compressed air to blow dust out of the fan motor, and should clean the blades, grilles, and frame as best you can before replacing the filters.
High PFR furnace filters aren't cheap. At a typical big box store, two high-PFR filters of adequate size will cost you at least $35 to $40 USD. You can bring down the per-filter cost by ordering in bulk online, but that costs more upfront.
These units may not be practical for physically disabled people. If the prospect of picking up and (gingerly) carrying the complete unit is physically daunting, if you have limited fine motor skills, or if you have no way to carry the unit outside to change the filters, this is probably not a good option.
If you need a short-term air filtration solution, such as when there's a lot of wildfire ash in the air, these kinds of filters are relatively cheap and work well if you do a reasonably conscientious job of assembling them and changing soiled filters. However, over longer periods, their cost advantage relative to a HEPA filter air purifier begins to erode because the filters are more expensive and shorter-lived.
A HEPA filter air purifier costs significantly more upfront, and where the air quality is bad, they may be in short supply. However, they're much easier, and usually cheaper, to maintain. Generally, they have a "pre-filter" to catch dust and lint, reducing the load on the HEPA filter(s) so that the latter's useful life is close to a year. (The pre-filter needs to be changed about every three months.) Furthermore, the filters are internal, so you aren't likely to touch them or dislodge their contents except when changing filters, which usually involves just popping them out into a plastic garbage bag and wiping down the interior with a microfiber cloth before replacing them. That can still be a little gross, but it's nothing like the filth and effort of having to gingerly carry the complete unit outside and tearing it apart.
