Dread Lords and Twilight play quite differently. I'd start with Twilight right away, it also has a couple of interface improvements that make playing much easier (such as various automation setting for ships).

If you want the story, play the old campaigns. You can do so in Dark Avatar (it loads Dread Lord campaign as well), but not Twilight. The campaigns simply aren't designed to handle the unique tech trees and other features of the last expansion.

Personally, I never played the campaign beyond a mission or two during beta testing. I guess, if you just want to know the backstory, load them in the campaign editor and compile a print-out of the briefing and debriefings.

as suggested already (and because I am a huge fan of ToA) I would start with a sandbox game of that. set the Universe to small or medium and the AI to beginner. You may not win the first couple of games, though you may, but the trial by fire will teach you what you need to know.

The reasons I reccomend ToA in stead of the previous two is there were a LOT of updates in ToA. The AI was improved, the graphics, and there were a bunch of improvements to the Tech trees. Also, if you learn DL or DA style of play and then switch to ToA, the changes are so significant that you will have to rethink a lot of what you were doing.