Need to mention that HEPA is the preferred filtration system. HEPA Filters typically last 4-5 years in the larger units . Ionic filtration, "Ionizers" uses static to literally burn the lint, dust , dander and particles out of the air. Some are allergic to the soot it creates in the air. Ionic cleaners boast that you can wash the filter instead of replacing it but you cannot run the air cleaner until the filter dries.
If you are battling allergies start with a filter in the bedroom where you can have at least 8 hours of clean air per night. Add more filters to other rooms that are frequented later. Cover mattresses with a hypo allergenic cover, Get rid of carpeting, books and toys, dirty clothes hampers, and other dust collectors. Substituting leather for cloth upholstery helps, too.