DMC1 is a MUST, it's an awesome, I still play it from time to time, Dante looks way better there than in the DMC1 costume from DMC3, it's just different, weapons Ifrit and Alastor are awesome, I rather Ifrit to Bewulf, when I have Ifrit equiped I just feel safe, lol.
Nightmare betha e way coller than the DMC3 version.
Anyways, DMC1 is that game that get's you to dig Dante in the first place, and your DMC experience is not complete without it.
After you get it I also recomend you get DMC2 (and now everyone in the forums get together to murder me) the thing is the game is not that bad, Dante is more adult but still Dante, Devil trigger form is awesome, the only cons are the repetitive gameplay cause weapons are all the same, and the game beeing way to easy, and I don't remember much puzzling to beat levels, it's just walk by and kill.
But it's not so bad, just not as goog as the others.