Installing air filters in classrooms has surprisingly large educational benefits (2020)

MERV 13's are optimal for particle removal because compared to a HEPA some of the removal requires multiple passes but the filters are a lot less restrictive and allow higher airflow. Corsi and Rosenthal looked into this with the CR box and came to the conclusion its technically faster at clearing a room than using HEPA standard filters. For infections and damaging PM2.5 particles mechanical filtration with MERV13 is the best you are going to get.

You could also add potentially get a HEPA with a carbon filter which will get rid of volatile organic compounds which can also be damaging (but also just be the smell of food) but they don't tend to be as effective and depending on the mix of VOCs verses particles one filter may run out before the other and carbon really doesn't capture all that much or well. It is a good way to get rid of smell at least for a while.

There is a whole world of different standards for filtration for industrial and hazard chemicals which the FFP2/3 and N95 standards for Personal Protective Equipment respirators will lead you into if you want to go into that rabbit hole, but for a household typically its mostlt about Particulate matter, Volatile organic compounds and CO2. CO2 is about bringing in fresh air from outside.

Then when outside of the household N95/99 or FFP2/3 respitators do the same job in unclean air environments which is basically everywhere, outside or indoors in public places pretty much never meet the World Health Organisations levels for PM2.5 and often exceed CO2 (a proxy for re-breathing and a high change of viral infection spread) standards too.

for infections you can use UVC, which is something people often overlook, although of course that has its downsides