I’ve done that - moved out of a mold infested house into a brand new house and kept some but not all belongings. Can you elaborate on risks? What do I need to watch out for?
Anything that sat around a mold infested area is something you should look at closely, at least to proactively give it a thorough scrub and dry in a well ventilated area before bringing in the house.
An air filer with a real HEPA filter will help catch airborne spores but if you already have mold growth anywhere in the room you need to take care of that before blowing air all around.
Generally a DIY HEPA filter and a CO2 monitor should be enough to keep good air in a home which does not have water damage. If you have ventilation then remember to swap your filters.
We have mold in my family's basement downstairs too and I run the ozone generator a lot to freshen the air. But unfortunately parents would never throw out the things.
It might be a very easy fix before you start buying expensive solutions. Maybe you have old pictures of the house before there were problems and you notice there was actually a strip of garden all around the house instead of concrete or tiles.