I agree, with those who say Austin Air... I have the Pet Machine.
I wouldn't go with anything that makes ozone or ions as it has been reported to cause problems with birds. This eliminates a lot of choices.
If you really want to remove the dander and dust from the air you will need a filter and the best and most effective filter is HEPA. With a HEPA filter you are removing the pollution, allergens and dust from the air and you are not adding anything else to the air.
So there are plenty of HEPA filter machines out there but for it to work you will actually have to draw the air through the filter and that is where you really need to make sure you have a good machine.
A lot of the department store machines will show the specs for the filter which will be comparable to the higher end filters like Austin Air but the thing is that the machines doesn't always do a good job pulling the air through the filter. Lots of machines are "leaky" in that they suck the air into the machine and some of the air passes through the filter but a lot of it will exit through gaps and spaces without going through the filter. Therefore, the efficiency and effectiveness of the filter goes down. So the specs can be really misleading.
You are in effect just moving dirty air around and you are not actually cleaning the majority of the air.
The better machines like the Austin Air machines will filter 100% of the air that they draw in and will put out 100% filtered air.
A good machine will give you a noticeable difference in the air in the room. I can tell when I have my filter on or off just by the air in the room.
The great thing about the Austin Air machines is the filters last 5 years. So they are pricier but you only have to put money out every few years, not on a monthly basis like with many others.