Without giving too much away, Mass Effect 3 is like that. The whole "this could really happen, the Reapers really could be out there". It has a way more sci-fi story though, because they go in depth about the Reapers and who they are, very sciencey stuff. Talk to every person, listen to all the news pieces, read every datapad and the story is amazing, regardless of what ending you pick, because you get so deep into the lore of the universe.
I'd still pick up the ME Trilogy if I were you though, because ME 1 has the best story out of all of them. Though I guess you could download the Mass Effect 2: Genesis DLC. That's an interactive comic about ME1 that lets you make all the important decisions.