Have watched/enjoyed in order : Breaking Bad, LOST, Dexter, The Walking Dead, Prison Break, OITNB, House of Cards. All I care about is a show that has an interesting plot/story with good characters. Only interested in dramas.
Have heard of the west wing, but I'm not sure if I'd like the plot. It's about what goes on in the white house, right? I disliked House of Cards mainly because of the politic aspect that bored me. Too short. Would prefer a concluded series, or one that has multiple seasons up on Netflix. Will keep my eye on it though.
Black Mirror is pretty cool. It's sort of like a modern Twilight Zone, every episode is a short movie. Just something different to check out.
Friday night lights. Seriously I have seen all of the series you listed in the first post and this series is up there with them in quality.
If I were you I'd give it a try anyway. Aaron Sorkin is a genius writer. It's my favorite show ever. Other top recommendation on Netflix would be Luther. It's British so it's kinda short... really great, though. I also enjoyed Bloodline, The Killing, Grace and Frankie, The Wonder Years, the various Star Trek series (particularly TNG and DS9), and the BBC version of House of Cards (kinda prefer it to the American remake, actually). There's also Mad Men and Damages, both of which I wanted to like (and obviously many people do), but didn't grab me personally for whatever reason. And if you happen to have Amazon Prime, there's all their HBO stuff: Six Feet Under, Deadwood, Rome, The Wire, The Sopranos, John Adams, Angels in America.