Regarding Alan Moore's "Providence," I've found
this site extremely helpful and interesting. If you know Moore, then you'll know "Providence" and "Neonomicon" are filled with references to both Lovecraft's works and his own life, and I'm talking "deep cuts" here, not just Lovecraft 101 stuff.
Regarding Grant Morrison's "Nameless," I loved it, but also need to read it about 6 more times to figure out what the fuck was going on. Typical of the majority of Morrison's material, but confined to 6 EXTREMELY dense, confusing and fucked up issues. If you know a lot about obscure occult rituals and ancient Mayan mythology & symbology, maybe you'll have an easier first read. Otherwise,
this,
this and the remaining parts 3-5 may be helpful. He doesn't manage to cover the entire series, but these are a good start.
Regarding book suggestions, read Laird Barron, Caitlin R. Kiernan, Thomas Ligotti, any anthology edited by S.T. Joshi, any anthology edited by Ellen Datlow that has "Lovecraft" in its title, or look into the semi-recent annual anthology series "Year's Best Weird Fiction," currently on its third volume, with each volume having a different editor to spice things up.
Brian Lumley's Necroscope series...
"John Dies at the End" and its sequel "This Book Is Full of Spiders" by David Wong are an interesting take on cosmic horror... unspeakable atrocities borne of sausages & cold-cuts & other meats. Haven't seen the film adaptation of "John Dies at the End" so I can't comment on that one.
That's as much as I can handle typing on my phone now.