If you air quality issues primarily involve dust rather than other allergens or second hand smoke you may want to consider simply getting a furnace filter. For many people a furnace filter can give them as many benefits as an expensive air purifier.
A furnace filter is a great option if you are skeptical about the effectiveness of air purifiers. Chances are you may still be concerned about the quality of the air in your home.
Do you suffer from allergies? If so then a furnace filter is not adequate. Furnace filters are ideal for removing dust from the air and other larger air pollutants.
In order to effectively use a furnace filter you need to have a furnace fan running all day long. Filters need to be replaced approximately every 3 months. These costs -- just as those for operating traditional air purifiers -- do add up.
If you are looking for a short-term answer to your question regarding air quality in your home then getting a furnace filter is the cheapest and quickest way to find this out. Rather than buying $200+ air purifier you can simply buy a $15 furnace filter.