I would recommend reading them in pretty much the order he wrote them. While his stories all stand alone, Lovecraft's later tales do refer to characters and incidents from earlier ones; he even went so far as to have characters re-appear later (Richard Upton Pickman of "Pickman's Model" has a minor but important part in the later "The Dream-Quest of Unknown Kadath"; the narrator of "At the Mountains of Madness" shows up briefly in "The Shadow Out of Time"). Parts of "The Thing on the Doorstep" will make more sense if you've first read "The Shadow Over Innsmouth".

You can find a chronological list of his work at http://www.hplovecraft.com/writings/fiction/chrono.asp.

Reading everything Lovecraft wrote might not really be necessary, though. I don't find much value in his writings before 1920; and he did not reach his peak until 1926 ("The Call of Cthulhu", "Pickman's Model", and "The Silver Key" all date to that year, and much of "The Dream-Quest of Unknown Kadath" does as well). It wouldn't be entirely wrong to read everything he wrote from 1926 on, while picking and choosing among the earlier stories. But if you do, I would recommend reading all of the following pre-Cthulhu tales:

"The Statement of Randolph Carter", which introduces Lovecraft's alter-ego Randolph Carter "The Terrible Old Man", a rare amusing tale from the horror virtuoso "The Picture in the House"; I think the reference to Arkham in this story was the first "The Moon Bog" "The Hound" "The Festival" "The Shunned House" "The Horror at Red Hook"

Several of Lovecraft's other early '20s stories also repay reading, but I think anybody wanting to get a handle on Lovecraft should make a point of these.