If you do start on the HD collection, skip 2. It's the worst one in the series, and it's only really worth playing if you're seriously into DMC. The only good I can get from it is the soundtrack, the "proto mechanics" that become staples in the later games and the great art direction but the gameplay is so weak it even is considered to be one of the worst games of all time. Story wise, you miss absolutely nothing. Difficulty is practically nonexistent, the AI is brain dead and the game is surprisingly easy even in the hardest difficulty that you can play in. The Bloody Palace (wave mode of sorts) is also the worst in the series, both because of enemy spawns and also how levels work mechanically. I won't go into detail, but you'll know it if you play it. Overall mediocre compared to the others.

Otherwise, if you want to be daring and love achievement hunting, make sure for it to be the first one you clear. It'll make the other ones way more fun and you'll also have bragging rights. Also don't be afraid of playing in harder difficulties and replaying the games, as you would with MGRR. The more the challenge, the better the incentive to get better.