Is dmc1 a important game?

Like most people these days, I started with DMC 5, and loved it. So much I decided to play DMC 4, and I've finally gotten around to the hd collection. I'm playing DMC 1 at the moment, and I am STRUGGLING. I really hope this game gets the resident evil treatment because it's good but, it's just so dated and clunky to play. If I skip 1 and go straight to DMC 3 am I missing any important plot points? I don't want to miss anything major but at the same time I don't know how much I can put up with the difficulty of 1.