Start with Seed of Destruction, the first Hellboy arc. If it's not exactly great, at least read the second, Wake the Devil too. People have varying opinions on Seed of Destruction. At the time Mignola hadn't written anything, so he had John Byrne do the heavy lifting for writing. From then on he did it all himself and it turns out he's a great writer. I have no problem with Seed, but eh, fair warning.
And all Hellboy titles are either written by Mike Mignola, or cowritten/plotted by him. Basically all 100% Hellboy titles are him solo, usually on art. He's done a few others like Frankenstein Underground solo, but for the most part BPRD and others are cowritten by people. Mostly John Arcudi until recently. They've all been edited by Scott Allie too. So between Mignola and Allie there's a tight editorial flow throughout all the books.
I'm sure somebody will post the very large master image of a good proper reading order, as the series come out spread all over the timeline, yet they're best read in the order published due to what they assume you know and what they hint at in the near future of core "present" books like BPRD or such.
The actual comics are more serious than the film. Bit more noir and gothic I guess? Mike Mignola pulls from an insane amount of sources. British, Slavic, Russian, Japanese, South American, African, Celtic, etc etc mythology has all played a roll, all mixed with a healthy does of Lovecraft, Robert E Howard, and I dare say Jack Kirby.