Recommended filter: make sure the filter is HEPA and certifies for at least MERV11. For filtering virus carriers and bacteria, use a filter that's rated for a minimum of MERV13.  

Typical air filtration devices which cost ~£100 can usually filter out 100-200m^3 of air per hour. In comparison, This purifier aims to achieve 1000m^3 per hour. (the fan itself is rated for 1680m^3, but I have made a conservative estimate of 1000 due to filters adding resistance to the airflow)

This design has 4 replacable filters, and includes 2 carrying handles.

Hardware:

1x Large 250mm ventilation fan (250mm diameter, 300mm mounting plate, 255mm screw spacing. Often sold for kitchens):
https://amzn.eu/d/0aF1TzE7
4x screws (included with the fan, thread directly into the plastic)
4x Air filters: 
https://amzn.eu/d/09JN1nY6

Also requires 2kg of filament. PLA is suggested.

Total hardware cost: £82 ($112 USD)
Total cost including filament £102 ($138 USD)
 

If you only want to filter dust in a workshop, chosing a lower MERV rating can save you money. If using in a dusty environment, make sure to clean these filters regularly with a vacuum. These filters should be entirely replaced every 6-12 months with moderate use. Light use in fairly clean rooms (such as offices) can extend the life of these filters to 2 years or more. With heavy use, these filters should not be used for longer than ~4-6 months.
You can also add a pre-filter to extend the lifespan of this filter

When constructing, I suggest removing the big metal flaps on the fan as they restrict airflow:

you only need a medium sized phillips screwdriver to remove these.

Inspired by box fan filters like this, but made slightly less janky...

in the files, I have included the whole assembly as well as the components split up individually. I suggest downloading the whole assembly and splitting it in the slicer.