If I were to start playing X-Com 2 (Terror from the Deep), would I miss anything major, plot-wise, or can I simply jump straight to the sequel?
I originally played Terror From the Deep before playing the original X-COM, and I had very little trouble following the plot. Though they are related (some of the aliens from the first make an appearance in the second), you will be just fine playing the second first if you want to. There are some minor UI / Organization changes that make the second a little easier to manage.
I've played the first 3. While there is some plot that carries over between 1 and 2 you're not missing anything in doing them out of order. Psionics is greatly nerfed in 2--in 1 if you develop your psionic characters enough it becomes a cakewalk. (For a challenge I went into the final battle with no weapons at all. I was able to win the first battle without ever firing a weapon, I had to fire ONE shot in the second.)