I could see a lot of templates working here, depending on how exactly the scenario plays out.
!. We could of course go with something similar to Shepard, a fairly independent captain who is ultimately answering to the powers that be though. I think this is the most likely, especially if the game takes place shortly after the Milky Wayers arrival in Andromeda but I also think it would be the most boring option. It would be easy to construct a story this way.
2. If the game takes place a little time after our arrival (maybe one or two generations, than I could see an independent character with his own ship and agenda working very well. A Malcolm Raynolds kind of guy. We'd need a good reason why this guy gets invested in some sort of plot (all of which would of course weaken the freedom we have with the character) but I think it would offer a bunch of nice role playing opportunities.
3. If the game takes place directly after our arrival, I would think a John Crichton (Farscape) scenario would be really cool. Maybe we get separated from the rest of the ARK team in the beginning, maybe we get an Andromeda ship that uses completely unfamiliar technology, maybe part of our crew will be Andromeda aliens with weird customs and behaviors we don't understand at first. A confused protagonist, completely out of his/her depth, I'd like that. You could still roleplay how the character deals with it of course. Does s/he react secure and level headed or terrified, trying to get a drip on the situation with rationality with humor or aggressiveness? It would be up to you. Even the entry into the main plot with the typical "find a way back" (to the ARK guys, not the MW) scenario would basically write itself and can proceed from there to wherever the writers want.
Personally I would love something like 3, I would be happy with 2 and I can arrange myself with 1 (which I really believe to be the most likely).