Best Air Filter For Dusty Home

My mom turns 78 today, and when I asked her what she wanted for her birthday, she said an air cleaner. Something along the lines of one of those Sharper Image Ionic Breezes.

The problem with my mom is, to put it politely, her house is not very clean. She has over 40 years worth of junk stored in there. It's so bad you can't even close the doors and have to walk sideways in places. Three cats and a bird add to the smell and general filth. Our relatives won't stay in the house because everyone gets sick. O.K., that's a good thing. My eyes get red and I sneeze like crazy from all the dust, a problem I experience nowhere else. My sister can only stay in the house after taking a Claritin (spelling?) pill.

Please don't suggest I get my mother to clean the place or hire someone else to clean it. She is 78 and never listens to me. And, we did have some people come by to houseclean, but they quit!

Anyway, what would be the best aircleaner to capture a lot of dust and animal dander from the air? Smoke is not a problem, thank goodness. Noise would be a secondary factor, as would be ease of maintenance. Operating costs would also be a concern.

I've made previous inquiries about the Sharper Image units, and they got pretty mixed reviews, so I'm hoping there is something better out there. It seems the Honeywell HEPA filters are kind of a standard, does anyone have any experience with these? Also, I've heard some good word of mouth about two air cleaner Costco carries: the Breeze AT for $550, and the Living Air Classic for $669. Anyone know anything about these models?

Anything you could tell me about air filters would be greatly appreciated. If possible, I'd like to keep the price under $700 since I'm not exactly drowning in cash these days.