I would consider taking the bus. This is by far the cheapest option!
ADO runs a direct first class bus from Cancun airport to the ADO terminal in Playa del Carmen which si right at the fery terminal. Cost is something like 100 pesos per person.
If you arrive at the wrong terminal you just take the complimentary airport internal bus service (driver will help with your luggage) to the terminal where the ADO bus leaves (not sure which it is), buy a ticket at the counter and hand your luggage to the bus driver who will put it in the luggage compartment of the bus.
Cozumel ferry terminal is just one block from the ADO bus terminal and taxis can not get any closer to the fery terminal than the bus (perhaps 300 feet closer).
Fery is something like 170 pesos per person one way. It does not make sense to buy return tickets as they are not cheaper and you are then bound to one fery company. I would just walk up to the counter, look which fery company operates the next fery and take that one.
At the fery you check in your luggage like at an airport and receive it after arrival. Upon arrival take a taxi to the hotel. The ferry only carries passengers, so a taxi or airport transfer van would not be able to go on the ferry with you. (I think there is another Cozumel ferry south of Play del Carmen that also carries cars, but using this fery with your airport transportation van would probably take much longer and be way more expensive than using the passangeer fery)
If you use a airport transfer company it is only the way from the airport to the van that is a little easier compared to taking the bus.
The van will not get closer to the fery terminal than the bus, so the only convenience would be if the van driver would help you to bring your luggage to the ferry terminal checkin which you would have to do yourself if taking the bus.
Taxi - fery - taxi is the only way to go from Cozumel back to Playa del Carmen.