I LOVE H.P. LOVECRAFT!
The suggestions that people have given you are rather "advanced", IMO. If you are a major sci-fi/horror fan and very experienced in reading this genre, then yes, you will enjoy them. As a young teen, my husband loved "Dream Quest of Unknown Kadeth," and also Lovecraft's poems. As an adult, I still find these pieces difficult to settle down and read. They have a lot of atmosphere, but not enough plot.
Also, there are a couple of ways to approach Lovecraft. Many people take pleasure in getting involved in the whole "Cthulhu Mythos" thing, and devour the entire body of literature. For them, it's like a scary version of Society of Creative Anachronisms," an "alternative world" that they can play around with.
You can certainly do that if you enjoy role-playing and that kind of thing. My husband enjoys Lovecraft in this way.
But another way to approach Lovecraft is to keep the Mythos in the back of your mind, but enjoy the stories as individual tales. Yes, many of Lovecraft's stories are part of the Mythos and contain hints of Cthulhu and the Old Ones and the Deep Ones. But they are still good stories even if you have no clue about the Mythos and all the connections. I personally enjoy reading Lovecraft like this.
Here are my favorites, and I read them several times a year.
The Shadow Over Innsmouth -- this story/short novel has it all! The young hero, the fish people, the isolated small town, the scary mystery cult ("the Esoteric Order of Dagon"--doesn't that sound scary?!), the creepy hotel with shuffling noises, the drunken but over-wise sot, the thrilling chase, the awful revelation, and above all, the super-surprise ending! Get this story and have fun! I've read it a thousand times at least. I love it! I think it's one of the best stories in American literature. I admit that I use the hyperbolic language style in my own fiction writing. My husband and I enjoy picking out people who have "the Innsmouth Look!" And we joke about staying at the "Gilman House." Read it! Love it!
The Dunwich Horror--I like this one because one of the heroes is a senior citizen. Cool.
The Outsider--this one is very sad and highly-underrated. I think teenagers should be required to read it. It says more about being an outsider than many of the popular teen novels say. Very Poe-ish style in this story, quite different than other Lovecraftian tales. Many of Lovecraft's stories seem to be told "with a grin," IMO--he is having fun with with his readers. But The Outsider is sad and soul-filled.
In the Vault--oh, my! This one is sooo much fun!! It's perfect for Halloween, but don't wait until next year to read it. It's the kind of story that kids tell during summer camp or at a slumber party. It's reads like an urban myth. I'm guessing that Lovecraft heard this tale from townies and decided to embellish it into a full-fledged story.
Pickman's Model--this one made it onto Night Gallery in an almost word-for-word re-telling. Great imaginative story, and it will scare you away from subways (not the restaurant) and Boston.
The Thing on the Doorstep--this is one of the creepiest stories that Lovecraft ever wrote. Probably my top favorite and probably the story that scares me the most. It's a morality tale, IMO. This is what can happen to college students who delve into matters best left alone.
The Rats in the Walls--of COURSE I like this story. The hero is a cat! Any story involving "eating" is bound to be good. What the protagoinist eats will be yours to find out when you read the story.
The Colour Out of Space--this is a science-fiction story that was years ahead of its time. You might not want to drink tap water after reading this one (bwoo ha ha!). Extremely well-written. IMO, this one starts simply enough and then builds and builds and it's still building, IMO. Disturbing. It could happen. Maybe it has happened.
A lot of Lovecraftian stories have been made into movies, but IMO, none of them capture the stories. I would LOVE to see someone do Lovecraft's stories for television exactly as they are written. Do you remember the Jeremy Brett Sherlock Holmes stories that were done by British television back in the 1980s? These were, for the most part, word for word out of the canon by Doyle. I would love to have that kind of re-telling of Lovecraft's stories, including the hyperbole.
The biggest criticism of Lovecraft's stories that I have seen is that they are silly. I don't agree. I think they're fun, definitely. But not silly.
I hope these suggestions are useful to you.