Pandemic is another co-op game that's easy to pick up for new players. The one bad thing about co-op games is if there are mostly experienced players and one new person then the experience people will usually influence the new person a lot and cause them to not learn much.

That's true with "total information" co-op games like Forbidden Island and Pandemic (or Flash Point, which is another great one).

"Codenames Duet" though is an example of a co-operative game where the two teams are working together but have to make their own decisions - it's also very easy to pick up for new players, I highly recommend it.