It has been assumed that according to various sources and artbooks that Devil May Cry's red-headed stepchild DMC2 fits in the timeline right at the end, that is no longer the case, the official timeline as of DMC5 is now:
3 > 1 > 2 > 4 > 5
Yep, we’ve changed the order - Dmc4 now comes after DMC2. ^^;— Matt Walker (@gypsyOtoko) February 7, 2019
So Dante's broody phase is now set before his first meeting with Nero. It seems the anime fits between 1 & 2 now.
Love those remixes of the classic tracks.