You want a HEPA filter to clean the air, and to use in the ShopVac. Regular filters will just circulate the dust.
http://www.maxprorestorations.ca/produc ... er-rental/
https://www.homedepot.ca/en/home/p.hepa ... 03772.html
You can also get as fine of a filter for your furnace as you can, which may help as well. Just change it out a month or so after your reno's are complete. We turned our HVAC system off while we were doing reno's, in an effort to not fill our ducts with gunk. Not sure if it worked, but...