Okay, I first played the series with Devil May Cry 2 in passing. I wasn't impressed. Then I learned that in the rest of the series the plot is more coherent and Dante is way cooler. I'm glad I believed them. In terms of characters and their interaction, it's second only to number 3. Dante, the hero, the mysterious woman who wrecks his office (now a pattern) and the Black Knight Nelo Angelo. Dante's past is unraveled as the game progresses, as are everyone Else's, which all tie in in many clever ways. Then there is the Dark Emperor Mundus, smote by Sparda, the legendary Demon who woke up to justice and saved the human world from Mundus' hordes. In terms of plot, it's great. A mercenary demon hunter is brought to an island where the Dark Emperor is gathering his power, and so on (play the game if you want the plot, it's more fun!) The cut scenes are excellent, as is the writing. Dante's demonic heritage gives him physical resistance that makes for some "interesting" scenes.
10/10, just in case you missed that above. If you haven't played this yet, do it.