I wish I could give a real answer but evidently games like this require multiple playthroughs and I've only finished each game once since I only got into them two months ago. I think DMC5 had the best initial impression but that's not saying a lot when recency bias + hype exist.
I'll just say that the positives for each of the three contenders are roughly as follows:
DMC1:
+Best Atmosphere
+Possibly one of the best instrumental battle themes in gaming
+Possibly one of the best instrumental ambient themes in gaming
+Arcade-y mission structure
+Bosses all feel connected to the island in a very natural way
DMC3:
+Best boss battles in the series, and probably even a game with some of the most consistently great boss battles ever, even if some of them are not that good (Centipede and Shadow Dante are so unoriginal!)
+A challenging game that feels very rewarding to complete missions in.
+Best emphasis on orbs in the series, how well you do in the missions can completely change how powerful you are very easily, you really have to go for those stylish points and get all the secret stashes
+The crunchiest combat in the series. I kind of wish that DMC5 found a way to make combat as crunchy and non-floaty as it is in DMC3.
+The most weapons and styles in the entire series
+Benefits a lot from focusing on Dante over other playable characters
DMC5:
+Probably the most consistent soundtrack in the series, so many bangers and quite a lot of great ambient tracks
+The best set up for a villain in the series, even if there's a little too many encounters with him before his last two forms (the Dante encounter in particular was unnecessary and I kind of wish they'd just skip straight to the cutscene)
+Obviously the most diversity in character selection in the vanilla entries of the series (though I guess DMC2 technically has Trish as an unlockable, but that's not as fleshed out)
+Perhaps Dante's best roster of weapons even if there aren't as many as in DMC3
+V was a great character
+The little nods to the rest of the series are great and I'd argue Lady and Trish's inclusions were better in just a single few lines then in the entirity of DMC4, even if both games needed to use them more.
