I have a dwc with drip rings I have plenty of air but I was wondering how important of a role circulation plays in root health. I haven't seen any comments specifically on that.
Circulation of water is key.
Thats why most of us DWC users have evolved to an RDWC setup. Note the R standing for RECIRCULATING. The water is pumped through a manifold and delivered to each bucket/site via a waterfall which eliminates the need for air pumps/stones entirely.
So if you're doing a single site system, really just using air stones at the bottom is your best bet. But a drip ring, in MY opinion, is completely pointless. The roots pull up all the water they could ever possibly need as they're completely submerged in water already. So I don't see any use for a drip ring to drizzle water over them from the top, too.