You have all the content trinity has, but you can't play trinity without the Rebellion content. Its not a modular package like trinity was.

All the story in this game is in the intro cinematics, the manual and on the lore section of this website (as well as in the in game text in things like ship descriptions and tech trees). The Rebellion into cinematic is the best by far, but you can find the Original and Diplomacy/Trinity intros easily on youtube. The manual is in a PDF in your Rebellion steamapp folder (it hasn't actually been updated for Rebellion, so its the original one).

Edit:

Original

Diplomacy/trinity

http://www.youtube.com/watch?v=UHotcVdqEBo

There is no single player campaign. Sins has never had one. Its more like an old 4X game like master of orion, the story is your gameplay. Or in the words of some disappointed players, its only "Skirmish mode". Though that is extremely underestimating this game.

The only reason I would get trinity if you already have rebellion is so you can start playing mods right away (probably not ideal for a new player) or for a bit more polished intro experience. Or the ability to play a game without any AIs while you learn, but this map can in effect fix that problem.