The sonic breeze is crap. A good HEPA filter might help with your dust problems... Honeywell makes some that are a good value (in the $200 range). Top of the line air filters (AllerAir and Austin Air) will run $400 or more. You might also consider a "fully sealed" HEPA vacuum cleaner but they are very expensive (e.g. Miele canister vacuums cost in the $700+ range... but they kick ass). The "fully sealed" part is important because most of the cheaper HEPA vacuums you see at Wal-Mart, etc., have a HEPA filter but it's not properly sealed so a lot of dirty air bypasses the filter and goes right back into the room, up into the air...
However, if your house is getting dirty from your wood stove, there's a very good chance that your stove and chimney system has a design flaw that you should fix before you think about getting an air filter.... Stick your hand in the firebox when it's cold and feel the air... Do you feel a cold backdraft? If so, you have a problem, and it's probably putting so much smoke and dust into your house that I don't think an air filter will help much. My mother in law has her wood stove chimney installed on the low section of a cathedral ceiling in a 1-story section of a 2-story house. That's a major design flaw and it creates a backdraft that fills the house with smoke when starting a fire and also when restocking the firebox with wood...
I copied and pasted a section from the woodheat.org website below that explains what I'm talking about... Hope it helps
Selecting and Locating a Chimney
If you feel cold air when you open the stove loading door and reach inside, your chimney is in cold backdraft. If you go ahead and light the fire without correcting the backdraft, you will fill the house with smoke. You can neutralize the negative pressure that is driving the backdraft by opening the closest door or window to outdoors. Note that the cold backdraft is the result of a system design flaw: either an outside chimney or a chimney that penetrates the building envelope below its highest level. In extreme cases, these flaws can result in hot backdrafts that fill the house with smoke. If your system suffers cold backdrafts, please be aware that it is more than just a nuisance – it can be hazardous. By opening the nearest door or window, you are merely masking the problem and as soon as you close it, the negative pressure will again act on the system, tending to reduce the net chimney draft available to flow the exhaust up and out of the house.
see also:
Wood Stove Design Best Practices