Most people do not start with CADR charts and technical specs. They start with a problem. A dog sheds a lot. Cooking smells hang around too long. Pollen gets in from outside. Or a room near a busy street seems to collect fine dust again and again.
A home air purifier is not magic. It does not replace ventilation, regular cleaning, fixing moisture problems or removing the source of mold. But for airborne particles, many modern units can make a real difference in the rooms where people spend the most time.
For normal home use, the common setup is a portable room purifier with a fan and layered filters. Air is pulled in, passed through several filter stages, and pushed back into the room. The real differences are in airflow, filter design, odor handling, sensor quality, noise and how well the unit fits the room size.