Some good suggestions above, but I wouldn’t put “Pickman’s Model” in the first tier. I see it as one of a kind and would suggest that you save it—and savor it—when you know Lovecraft a little better.
I love his erudite vocabulary. I don’t know of any other author who can touch him for that, although Michael Chabon does make me look up some words. One word you’ll find in a Lovecraft story more often than not is blasphemous.
A paperback anthology would be as good a place to start as any.
I started reading Lovecraft at about age 13, probably as an extension of my love of Poe. A few years ago I got, cheap or maybe free, his complete works for Kindle. Started at the beginning and just kept going. Some of the stories could have been left in the drafts pile and not been missed, but I read ‘em anyway.
One word of warning: Lovecraft harbored some extremely fierce prejudices and exposed them in his fiction. Modern generations are apt to feel compelled to look away when they show up; they are hard to read. But I would not abandon his works because of that. I’d just be prepared.