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Most of the stories are relatively independent... there are a few recurring characters and such, I think there may be some order you're supposed to read the Carter/Dream stories in, but they largely stand by themselves, anyway. I think "Pickman's Model" gets referred to in other stories a bit, too, but none of the references are really "spoilers" more just "crossovers." The serious connoisseurs like Greg, Erich, Graeme, and Toren may scoff at me for not knowing the One True Order to Read Them, though . My vague recommendation would be that if you liked Innsmouth, you should move on to "The Haunter of the Dark" and then tackle "At the Mountains of Madness," but I'm sure others would have different recommendions; I'm sure you'll get a lot of advice if you re-ask this over in the Cthulhu forum, too. I think there was a thread about "favorite HPL stories" somewhere around last year, too.
Oh, Monty...why the rolling eyes?
There is no particular order to the mythos, in fact, like most religions, there are a lot of contradictions ! Be sure to check out the newer stuff to, by Stephen King and company...Tales of the Cthulhu Mythos is a good book to pick up, it kind of runs the gamut.
Boy, I was gone from Tonmo way too long, folks, I totally missed this.
Heather, you've got to read The Thing on the Doorstep, if you haven't already. One of the best relationship stories ever written.
As for order, really not important with HPL for the most part. Read The Cats of Ulthar and Pickman's Model before you read Dreamquest of Unknown Kadath, and The Thing on the Doorstep after Shadows Over Innsmouth and you ought to be fine.
Incidentally, Barnes and Nobel currently has a gigantic hardcover H.P.Lovecraft collection in the bargain classics section right next to Wells, Austen, etc. Under $20.00 US, and quite complete, if you want a portable version with just about near everything. Unfortunately, this won't help you out Heather, as it's exclusive to Barnes and Noble here in the USA, but you might find something similar at Chapters.