One of, if not the, easiest way to contribute to the current Quarterly Project is through StreetComplete. For anyone not aware StreetComplete is an editor on Android, it’s designed to be incredibly simple and help introduce new users to contributing to OSM. It’s how I started regularly contributing.

Some of it’s questions (quests) displayed to users are directly related to the current Quarterly Project like asking if a given road has a cycle path, and categorising types of bicycle parking. So if you were exclusively interested in the Quarterly Project you could disable the other quests and focus on the ones above.

However some of the other quests indirectly help OSM cycling data, such as road surface, whether the way is lit, names, one way, speed limits, crossings and pavements. They are all incredibly useful to downstream users of OSM cycling data. I think I recommend starting with all of the quests but disabling some high traffic ones, such as building types, you can, and should, come back to them, but if the amount of quests is overwhelming there is no harm hiding them until later.