I felt the 3rd game really went back to the first, drawing on the same feel, going back to the same locations, discussing people we got to know in the first one, and even explaining some of the inconsistencies in the original story.
So I was really happy I played the first one, even if I absolutely hated quite a bit of the gameplay when I did. I even gained more appreciation for it while playing Black Mirror 3.
I picked the game up online at Adventure Shop, but had to patch it with other files to get it working. If you buy the online version I still have the working gfx files you need to patch in hosted here:
working gfx files [dropbox]