Should I watch DotD or NotLD (or any other movies) before watching SotD? Are there references that I will miss?
No it is not required
As has been already mentioned by several, you do not need to have watched any other zombie movies to understand the plot of Shaun of the Dead. It is a stand alone movie with its own plot that is completely contained within itself.
Yes it will add some understanding of certain jokes and references
While it is not necessary to have seen other zombie movies to enjoy Shaun of the Dead, it is after all a parody of the zombie film genre and does include a number of jokes and references to classic zombie movies such as Night of the Living Dead, Dawn of the Dead, and others.
I personally saw Shaun of the Dead before I had really seen many other zombie movies and over the years I have become a big fan of them and watched several classics repeatedly. After having rewatched Shaun of the Dead most recently in October 2016, there were quite a few jokes and references that I hadn't understood, or had missed previously and it was fun to catch those references.
No. As has been suggested in comments, Shaun of the Dead's plot doesn't really parallel or spoil Dawn of the Dead. You can safely watch it without spoiling either the original or the remake of Dawn of the Dead. As I recall, its tagline was something like "a romantic comedy, with zombies."
I would also ask if you've already watched Hot Fuzz and The World's End, and if you're a fan of British TV comedies, specifically Simon Pegg and Nick Frost's show "Spaced"?
They have a niche humor which makes their movies and shows more funny once you've got a feel for identifying it. If you haven't seen any of their work, I'd recommend Spaced. As others have said, you don't have to have watched Dawn, or really any zombie movie, before watching Shaun of the Dead, and it's not because of the references, but rather the style of humor that they use.