Best dehumidifier and air purifier combo for $100?

I don't want to seem dismissive, but you've just asked for two appliances to combine into one, and for them to be good, and priced less than even a decent quality for either. You're putting far too many filters on your search. It will be difficult to yield a result like this. It's difficult to find a decent dehumidifier anywhere near $100 at all. And to have that also be an air purifier is likely impossible, because the filtration systems are completely different.