Playing through the series for the first time, need advice

Title!

When I was a teenager, I played thru DMC4 without playing thru any of the others though I forgot a lot about the game. So, I saw the entire franchise is on sale on PSN right now for $50 and just bought all of it. I plan to start with DMC1 tonight.

I just have a couple of questions. Going thru the games for the first time, is there anything I should be aware of? Story and secrets I might miss, optional content I should do? I also know one of the DMC games is notoriously awful. I can't remember if it was 2 or 3. What's so bad about it, and is it worth playing at least once for the story or better off skipping it?

I played DmC: Devil May Cry and I actually did like it, though I'm excited to play the actual series now once people have given me some "guidance" on how to best enjoy the games for the first time. Thanks.

EDIT: Oh, also, is it advisable to do every game on the hardest difficulty your first run of it? I play most games on the hardest difficulty and am pretty decent at action games like DMC.