I know, a lazy approach, but my story would be something along the lines of:
1. Full fledged expedition (scientists, inventors, psychologists, biologists etc.) to a far away star went bad - the ship got caught in "interdimensional fracture/wormhole" and was spat out in a different part of the galaxy.
2. You drift in an unknown space on a damaged vessel with lost hope and depleted supplies when your radar goes "live".
3. You get picked up by a humanoid ("local humans") race "A" that seems not to be aggressive and actually pretty hospitable. They bring you over to their home planet as a guest. But it doesn't feel right as they are stalling your repairs and resupply under the guise of cultural exchange, making you go around their planet showing off their cultural advancements.
4. With time you get scraps of information on the situation in that space locale. It turns out to be that there's a war going on between races A,B,C and races D,E,F. Reasons for war are X, Y and Z. They aren't black and white, not clear cut. It also could be a disinformation by your host.
5. You get the feeling that your guys aren't really on the "right" side of the conflict and you start planning a long and hard escape. Your host don't suspect you yet.
6. Soon, a massive biological attack on your captors home planet happens, during which you and part of your crew manage to escape to an orbital station that's badly damaged and completely wiped out of race "A". You are unaffected, 'cause your biological composition is impervious to that biological weaponry. The attackers leave as suddenly as they appear, not noticing you.
7. You start to rebuild and help to revive race "A", since without their help you'd be a dead meat in a can floating about the unknown space... You find a few race "A" survivors on their home planet (some bright minds hid in a super secret nuclear blast bunker that you found after the bio-attack aftermath... w/e) and re-engineer their DNA with yours to preserve their race. They cooperate and with their help you resurrect the orbital station and build a one of a kind, cutting edge tech space ship to get back home. All you need to do is find that wormhole through which you traveled here. You are not interested in the local conflict. You just want to go home. Meanwhile a very strong bond between humans and race "A" was developed.
8. You go out in an approximate direction of where you came from..... Stuff happens - you meet another race. And another. You can't find the wormhole. Blah blah blah. Some more stuff happens. You're looking for somebody who knows how to get you back home. Conflict plot thickens. Even more stuff happens. You get sucked in the conflict......
9. You find out that you can't get back home the way you came here, but you can through some old nonfunctional Star Gate/Relay/w/e found on the other end of your galaxy sector. All you need to do is make it function.
You can beat the game by:
1. Fixing the Star Gate and teleport back to Sol, staying neutral in the conflict. (To repair the thing you'll need parts, resources, both material and "human" and huge source of power... w/e.. The adventurous path) GREEN EXPLOSION
2. Solving the conflict and get help from whoever you helped in the conflict. (This is another way to fix the teleporter with a lot of diplomacy and the conflict story. The storytelling path) BLUE EXPLOSION
3. Conquering the races and making them fix the Star Gate for you. (The "alotta fighting" way) RED EXPLOSION
And it'd also be nice to beat the game with the combination of those.
It'd be next to impossible to beat Shepard's space Jesus story, IMHO, so I'd not even go there.