All of his stuff is just short stories. They only connect to each other through references to people, places, books and the pantheon of monsters. Some of the Dream Cycle stories contain the same characters, and so could be said to follow each other based on that. But otherwise the stories don't really connect to each other in plot. If there was any order it would just be the order in which they were published, in which case the stories usually take place around the same time that they were written, with maybe a few exceptions.
The Nameless City (1921) is the first Cthulhu story. It is about the author of the Necronomicon. The next story, The Hound (1922) first mentions the actual book, which is the basis for most of the connections between the stories. If there could be said to be one reoccurring story it would be that in each successive tale we learn a little bit more about the book and about the Great Old Ones. The Call of Cthulhu (1926) is the only story in the Mythos written by Lovecraft that actually features Cthulhu, although I think he is mentioned in a couple others.
It's funny because the Necronomicon is supposed to be this rare book that there is only like 2 or three copies of, yet somehow no one seems to have a problem getting a hold of one in every story.