I just bought my son a new Yamaha Rydeen 5-piece drum set with a 20" kick. As you would expect from a drum set in the $500 price range, the heads on the set aren't great, and produce a lot of ringing.

What heads would you suggest as a decent upgrade to a starter set like this?

I have a older Yami- the G2 sound amazing live or in the studio.
Those heads they are what i call shipping heads.
Go see Jay at CD and he will take care of you. Please tell him Chris fron RD.com sent you.
This kid knows his stuff. Also try cranking the heads a bit,this should reduce your noise. Remember to tune it like a tire on a car.
just a bit then direct accross head to the other lug.
Tell your kid congrats on the new kit.