Sorry for your loss. You have received a lot of good advice. I can comment on the air filter question. I have these 3:
http://www.amazon.com/Honeywell-50250-S-99-97%25-Round-Purifier/dp/B00007E7RY/ref=sr_1_1?s=kitchen&ie=UTF8&qid=1380085636&sr=1-1
This one is good and easy to clean using a vacuum, but a bit loud, even on the low setting and it put out a lot of air, like a fan...
http://www.kenmore.com/kenmore-plasmawave-trade-large-room-air-cleaner/p-03285450000P?prdNo=11&blockNo=11&blockType=G11
This one is the one I currently use where my greys cage is. It has an auto sensor and it is also easy to clean using a vacuum. I don't think I could sleep with this one in my room though, as the motor doesnt idle at the same sound... Does that make sense lol, it goes up and down up and down. But I am a light sleeper.
http://www.rabbitair.com/biogs-ultra-quiet-hepa-air-purifier.aspx
This one is the most expensive, and the quietest, looks like they are coming out with a new model. I use to use this one but I need to replace the filter and carbon screen thing and just haven't gotten around to buying new ones. This one was the most hastle to clean since you had to rinse the carbon filter out and wait for it to dry. And you also have to turn off the ionizer feature.
The air filters that I feel collected the most white dander/dust and down feathers was the Honeywell then the kenmore then the rabbit. The rabbit has a white screen so you probably can't see all the dust like you can on the black screens. They all work well though.
Good luck!