Agree with the above posts, vent to the outside for complete removal of all fumes. For my use the spray booth has a powerful in line fan, lots of air flow, filter is the full size of the back of the booth. Fan is explosion proof. Four inch flex metal duct takes air to outside of garage.
Regardless of paint type, the cleaning agents you will use for cleaning airbrush, brushes, tools, etc, will likely be as harmful or maybe even worse than the paint itself. Best to get those agents out and away from the house, simply moving them to another area is not a reliable solution.
My booth is home made, the filter gets lots of residue buildup on it, so to be cautious I remove it from the booth and store in a big sealable plastic bag, until next use. The filters are about $3.00 at the hardware store, so I just change them frequently, about every ten painting sessions.
I think a filter contaminated from use is capable of leeching risky fumes, even though less than those from painting or cleaning, so keeping them sealed between uses seems a good practice to me. Just a suggestion, but don't forget to wear a mask while painting or cleaning. You're only issued one set of lungs.
Patrick