I think DMC is a great game too, but i look at him more as a great adventure game than a great hack'n'slash. The level design, puzzles, mechanics all are great and introduced some really cool things to the franchise as concepts (sword-cancelling in Nelo Angelo battle is freaking cool, you can clash swords with him and can win without that QTE things, using your skills). He served as a powerful and rock solid foundations to what they would bring to us with the entire franchise, and had much more of that "developing" in the level designs through the game, you are seeing in the actual levels what is happening as Hell becomes more "integrated" with the human world, they tried to simulate this too with the rise of the sins in DMC3 but just no worked so well compared to how it was in the first DMC.
As for Dante's personality, i like him too in DMC and the way i like to see this is: he's much more tense and serious in that stance, he doesn't how who Mundus is, but he knows that he's a very powerful being, the most powerful being of Hell besides his father. And he go to that mission knowing that he can have his revenge on that family matter, but just in the first cutscene the game show his sense of humour when he acts like he's weak and is getting a spanking from Trish when she tries and "fight" him. And he just get up and show how powerful he is.
I do not like the DMC2 Dante, but it's like a "natural" evolving of a powerful and "immortal" being. I mean, the cutscenes shows how overpowered Dante is in that game, he becomes apathetic while beating demons and that weak things. It's a shame to see someone talking about humanity and how humans never surrender on the end of the first game becoming a silent and apathetic guy.
I like how Dante is in DMC3 and DMC4. It's very entertaining to watch he doing his crazy, non-sense and "i don't give a flying ****" things. The dialogues with bosses like Cerberus and Beowulf are awesome too, and the Beowulf one contributes to his development when he sees that he cannot hide from the truth of his father being this guy who messed up with and drived that demons so mad.