Is A Hepa Fliter Air Purifier Or Ionizer Be Use Low Astma People?

I am trying to decide what machine type be best for a low to medium astma person and also another person that is allergy to grass after it cut.
Is a Hepa Filter Air Purifier the best one to get or a Ionizer.
I was planning on getting a Hamilton Beach 04491 True-Air Tower Air Purifier or the Hamilton Beach Air Ionic just needed to know which one be the best. The person is a 5 year old.