Essentially, HPL did three types of stories- standalone 'horror' stories, Dreamlands stories (which read more as fantasy) and then the 'Mythos' stories, which had a shared continuity with each other, and with some stories and elements that other writers in his 'circle' were doing.
If you are looking for actual books to check out... there are the softcover Del Rey collections, and the hardcover Arkham House collections.
I'm not too familiar with what is in each Del Rey book, but with the Arkham House collections, I would recommend starting with The Dunwich Horror and Others.
It gives you a good mix of the macabre stories and mythos, and includes most of the major mythos stories he did. No Dreamlands tales in this one though. For those, you have to hit the other two collections.
Dagon and Other Macabre Tales collects many more short stories, mainly a mix of Dreamlands and macabre tales.
At the Mountains of Madness and Other Novels collects his longer works. You have pretty much all three types in here, including the main Dreamlands story (Dream Quest of Unknown Kadath).
There is a fourth one- The Horror in the Museum and Other Revisions. These are works that other authors submitted to HPL for him to revise, or that he ghostwrote for them.
If you don't mind reading stories online (I can't do it myself, I prefer physical books), this link will get you to the HPL page on Dagonbytes that has pretty much all of his works online except the ones he revised or ghostwrote.
Have anymore questions, just ask!