I am a newbie too, but once you have Twilight of Arnor installed, you can launch it and play any of the three campaigns: Dread Lords (i.e., the original GalCiv II), Dark Avatar, or Twilight. For the sake of the story, after getting some experience via one or more non-campaign scenarios, I would play the Dread Lords campaign before the other two. Since you would be using the Twilight launcher, you would be playing the most updated version of Dread Lords, and any tech trees available to you would be appropriate.

I've been playing since near the original launch of Dread Lords and have not found the campaigns that useful for learning the game. IMO, you're better off jumping straight into sandbox mode with the base game and looking at older forum posts here (and older pages at the wiki).

Let your own learning curve decide when you switch to the 1st & 2nd expansions--both expansions add significant complexity to the game, so starting at DL will 'cut you some slack' in a sense. There's also the question of just how much satisfying game time you want per dollar you spent--if you begin at DL and play until you feel like you have it down pat, and do the same for DA, you might find the new stuff in TA all that more rewarding.