From listening to people who seem to know what they're talking about, I think it's supposed to be after DMC2, because in the final shot Dante is coming back from hell on the bike that he took into hell in DMC2. Also, there're some brief shots where it looks pretty definitive that Virgil is the one who sliced off and took Nero's arm, thus necessitating its robotic replacement. Lastly, the new girl is the shopkeeper from the previous game(s).
Again, this is all from me listening to people talk about it, because I have also never played a DMC game ever.
that song has such a tacky mid-2000s numetal vibe and fuck am I ever feeling it
i haven't properly played a DMC game since the first one, which I was bad at. The teenaged mall goth in me always liked the aesthetic tho, and I kept up with the story/lore through lets plays and such. I might go back and play 4 to hype myself for this new one.
The series doesn't have a complex story and the story of each game is overall light in content.
Devil May Cry 2 is a quite underdeveloped game, specially on its bread and butter, the combat system. Hence why many fans say that you should ignore it, if you are interested in story just read a summary.