I have 5 cats right now. I'm always looking for good ways to keep the cat hair and allergens down so I can breathe without taking too much medication. Here are a few of the items that I've found which work exceptionally well. They help with both cat and dog allergies, as well as dust mites.
For vacuuming, use HEPA filtered units rather than the bagless style vacuums. Dumping a bagless unit just releases a lot of loose dander into the air. It is strongly suggested that when dumping a bagless unit you wear a respiratory mask. A central vacuuming unit is most helpful for people seriously affected by allergies. A great carpet shampooer is needed, as well. I suggest one that has tanks instead of hoses. You can rent these at supermarkets and other outlets. You can use these carpet shampoo units for deodorizing as well as removing allergens.
Be sure to clean or replace the filters on heating and cooling units at least monthly.
Never dry-dust. Always use something, either a spray wax or a dust magnet spray. Some of the newer dusting wands claim to attract and hold the dust particles. Try them to see if they work for you, but if they don't be prepared to go back to damp dusting.
I do not generally discuss specific products that can be purchased on the open market. However, I want to state here that "Swiffer" and "Pinesol" (Phenyl containing cleaners) are not injurious to cats or dogs if used according to label directions and all surfaces are allowed to dry completely. For further information, contact the manufacturer or check Snopes, the online urban legend dispelling website.