That big ship almost certainly won't be under our command. Most likely we will be in command of a smaller ship that serves that ship.
That is also along the lines of what I was thinking. I mean we know that we are going to play a "combat-trained but untested" character so clearly we have to report to someone. Shepard reported to Anderson/Hackett so whatever character we play (who isn't supposed to be as "all that" as Shepard was even at the beginning of the Trilogy) will need to report to someone.
If the leak is to be believed (no reason not to believe it at this point I think) we know that our ship will be called the Tempest, and we know that the Krogan race will have a colony ship, which presumably means that all other races will also have their own colony ships. It wouldn't make sense to make the trip to Andromeda as a fleet of ships (why have to worry about propulsion on multiple ships rather than only one) so if this is indeed the ark ship we saw in the teaser, it would have to be huge so that it can house everything the races of the Milky Way will need to establish colonies. At the very least it would have to have the capabilities of manufacturing ships, weapons, etc., so that we can execute our mission(s).
The question is, did the races of the Milky Way actually build this ark ship from scratch or was it an existing ship that was re-purposed? If the theories are correct and we are in fact fleeing the Milky Way because of the reaper war, I would think that we would be very reluctant to re-use reaper tech and bring it along with us...