Hah! We're not judgemental about such things. I'd recommend checking out some of the downloadable stuff on the PS4 - a lot of modern indie stuff is almost like Megadrive-era games but SO GOOD. Nuclear Throne, Broforce, Rogue Legacy.
In terms of "catching up" it's really hard to say what approach to take - games have become so broad now that there's really no correct critical path. Dabble with demos, perhaps? See what takes your fancy? If you're looking for a recent AAA must-play, I'd say The Last Of Us on PS4, hands-down.