Honestly, you don't have to but it is directly related to 3 and by extension of the cult, homecoming as well. Origins is something of a prequel, but if I had to choose, I'd go in for Travis and his story not the alessa stuff. 2, shattered memories, and downpour are more psychological horror, relying on atmosphere and aesthetics to emerse people in the game. My top 3 go: shattered memories, downpour, and 2.
As for four, it is something of a mix of the primal horror from the cult games (1, 3, and homecoming) and the thriller style of the psych games (2, downpour, and shattered memories). It is a great game, but before you dive into it, remember: it is about the villain, Walter. Henry, the playable character, isn't exactly the most fleshed out and is more like link from zelda.
It is a wonderful series, and I still find it despicable that people don't give shattered memories and downpour the props they deserve.