Most "shop vacs" have fine dust filters available or there are also slip-ons to fit most filters.
Just empty and change them as necessary.
Or , if you insist on an upright, regular bag changes would apply to even those bought from a pawn shop.

Thanks, Snoonyb. I figured I'd get a Sears shop vacuum. I didn't know they could do double duty outside of the "construction zone" with a special filter to vacuum the rest of our place.

You might want to consider a CleanStream filter for you shop vac. They do a heck of a job but inside and outside the work area. While they're a bit expensive, properly cared for they will last for several years.

Here is a link that might be useful: Gore CleanStream Filter

Mike_Kaiser, thanks for alerting me about that filter. I've not heard of it before. The video demonstration on that website was pretty impressive.

You might want to consider investing in a top-notch shop vac with a HEPA filter, like a Fein or a Festool. You won't even think of them as shop vacs, just the most powerful vacuum you've ever used. And they have real bearings in the motors so you won't be deafened when operating them for an hour at a time.
Casey