I'd say it depends on what you're looking for since I feel each DMC game has something new.
DMC1 is more survival, hack n slash where you really have to be on the ball with how you play. It's definitely challenging for the casual player and I would recommend taking the easy mode choice if you keep dying on Normal. Also get use to only using one green star for health cause that's all they're gonna give you.
DMC2 is damn near easy as all hell and pretty dull of a game. You'd be better off skipping it. Still, there's SOME use to it; playing Lucia is pretty fun compared to playing as Dante. You could get through that game with guns alone.
DMC3 is a fire of a good time with the combos and the insanity of it all. Dante's gameplay is the best it's been since DMC1 with the style system and the arrey of weapons to choose from. And that's just Dante; Vergil is just as good with the katana, and the gauntlets/greeves. It's awesome if you wanna get into some good ol' hack and slash fun.
DMC4 is great gameplay wise if you're still starting the series. Nero is limited in weapons and movesets, but he's still pretty fun to play with the pull and grapple mechanic in the Devil Bringer. Dante is even more fun with the DMC3 style gameplay but ampted up to an 11. You should definitely get the Special Edition and play as Vergil, Lady, and Trish as well with other costumes and faster gameplay.
And the of course there's the supposed black sheep (literally) DmC: Devil May Cry. Say what most will about the redesign and changes in this alternate universe/reboot, but it's gameplay is extremely fluid and tight compared to other Devil May Cry games. I would get the Definitive Edition of the game with all the costumes, Bloody Palace, and being able to play as Vergil. It's also faster gameplay like Special Edition.
All in all; I would probably suggest the ones you should play are DMC1, DMC3, and DMC4 so you can at least understand the story that leads to DMC5. Play DmC if you're looking for something a little more grungy and less anime-ish. As for DMC2...well you can just skip that.