I believe most people book a pre-arranged van. I flew into CZM and spent 4 nights at the Westin Cozumel, so my arrival into Playa Del Carmen was via Ferry.
I paid $50 USD for Andaz's SUV to pick me up, though a Taxi would have cost $7. I happened to be feeling nausea that day, and just didn't want to have to chance it with a taxi -- normally I would have just taken the taxi.
I believe they charge $100 USD for their service from the airport (which is also much more expensive than other options), but I will say their SUV is very nice and clean, and it is certainly a luxurious experience.
The Van service I used in Cozumel was extremely basic, and shared with a total of ~10 people (my wife and I plus 8 strangers, going to different hotels) and I'd expect the CUN van services to be comparable.
I believe Uber is available from CUN to Playa, but it is not available from Playa to CUN.