Which decks do I need to get that are based more on his stories rather than new Cthulhu Mythos stories, and which ones work well together out of them, or is this not possible to have? Trying to decide which ones to buy but I am new to the game.

A lot of it is pretty mixed together. Check out the early stuff though you will probably find more thing geared towards HPL's specific stories.

The base set and the new Ancient Relics cycle have more HP Lovecraft stuff in there. Other than that, there will be a few cards mixed in each cycle, but they are very few. This is a Mythos game which is constantly evolving and is based off of new stories.