GalCiv 1 has no campaign mode.

I don't have the Altarian Prophecy so I don't know anything about that campaign. I've been able to follow the storyline in GalCiv II very well without it.

I don't have the expansions either, but I actually feel that the DA campaign has the most creative storyline. Playing as the Drengin gives it a very different (in a good way) feel from the more typical "Humans must save the galaxy from Ultimate Evil!" DL and TOA campaigns. That said, I like the overall storyline too. It has flaws, but most fiction does. And if you only have Dread Lords (as it sounds) then I would recommend playing the campaign at least once, because it gives the individual races a lot more personality, which is something that they need in DL.

(Also, it's the only place in the game other then a couple of the scenarios where you can go up against the Dread Lords)