Yes, you have to present yourself at the check-in counter. The WizzAir website is pretty clear in that situation:
In case you have not purchased any seats with your booking, check-in will become available only 24 hours before departure.
- check in online
- print your boarding card
- present the printed boarding card at the gate with your travel documents no later than 30 minutes before the scheduled departure time
- if you hold non-EU travel documents, you need to present yourself at the check-in counter to have your documentation checked and your boarding card stamped
(taken from https://wizzair.com/en-gb/information-and-services/booking-information/check-in-and-boarding)
Unlike other airlines, it seems that WizzAir allows / expects you to do a regular check-in first and then present your passport at the check-in counter. My guess is that they have this step separate in order to make the actual boarding process faster if boarding staff only have to look out for stamps, not verify your documents.
As for the timing, the check-in counter opens 3 hours before departure, and closes 60 minutes before departure (this information can be found on the same site linked above). Keeping in mind that there might be queues, it's best not to cut it too short - arriving at the airport 70 minutes before departure could easily make you miss your flight - but if you consider 3 hours to be excessive, you're probably fine planning your day such that you arrive about 2 hours before departure. However, all this is done at your own risk - if you don't make it to the check-in counter at least 60 minutes before departure (and by "making it" I mean actually standing in front of the counter, not joining the queue), you might not be allowed to fly, so you better plan to arrive a bit earlier and have a nice coffee or meal in case everything goes smoothly.