Yeah, you can pretty much start anywhere. It's not that Cthulhu is the only one with a name, but it's just about the only one that has its own story dealing with it directly (the closest other one being Yog-Sothoth in "The Dunwich Horror"), and the only one with a solid description of its appearance.
Part of the point of Lovecraft's oeuvre is that the universe is vast and frightening and there's shit out there totally beyond the capacity of humans to understand and remain sane, so the stories are basically just fucked-up one-off experiences of horror without a progression of understanding, because there can be no understanding. As you read, you'll start to catch common names of objects and places and beings popping up again and again, giving a sense of a unified mythology, but there's no particular order to the stories where one clearly follows on another and it's not necessary to know the minutiae of the mythology to understand a given story. He wrote and published stories in magazines primarily, and wasn't especially famous in his own time, so he couldn't count on people reading one story knowing any of his other ones. References to what's now called the "Cthulhu Mythos" were basically just Easter eggs for his writer friends and for his own amusement.
The closest to a true progression would probably be to read them in the order in which Lovecraft wrote them, since that would follow the development of his own understanding of the greater mythology, but you can safely just buy any collection of Lovecraft stories and read them in the order presented (or read them online at Wikisource), since they're effectively unrelated.
Invid wrote:As a teen, I rented audio versions of both The Rats in the Walls, and a Stephen King short story. To my shock, the King was almost identical to Rats in the Walls! Luckily I was already a Lovecraft fan, but it did turn me off of King for a bit 
Probably half of King's short stories are "homages" to earlier authors' works. What's particularly ballsy about the way he does it is that the narrator will often remark on how their experience reminds them of an old story they once read, and directly name or reference the story he's cribbing from.