Just pick up a general "Best of Lovecraft" type collection: Chances are, it will have the biggies: "The Call of Cthulhu," "The Colour out of Space," etc. It's not really a series, with continuing characters or whatever, so you can read them in most any order, or even skip over a story that isn't working for you. (The last time I tried reading "Shadows over Innsmouth," I found all the phonetically-rendered dialect rather grating so I skipped over it. A little of that goes a long way.)
As for recent Lovecraftian fiction, can I shamelessly plug RED RIGHT HAND by Levi Black? It's about a young woman, a distant relation of H.P., who gets caught up in the nightmarish world of the Elder Gods. (Full disclosure: I edited the book.)
I also enjoyed MAPLECROFT by Cherie Priest, which ingeniously mixes Lovecraft with Lizzie Borden. (Haven't had a chance to read the sequel yet.)