The main ark could be a retrofitted Quarian habitat ship (or how they are called).
It would need to be far larger if it's travelling between galaxies. I'm not sure how dependent liveships are on basic solar system resources. For example, assuming they're able to grow some crops for food, do they need to park near a sun for a while? Intergalactic space on the other hand has nothing. Simply put, you're not self-sufficient unless you make it in dark space. And you need a heck of a lot to make it in dark space. Not even for technology, for simple storage. Even if you put everyone in stasis and you have very efficient power requirements for said stasis, you'd still need huge, redundant powers sources.
*thread derailment opportunity detected
Quarians are superior and ahead of the curve in all ways. It's the only explanation for having a population less than the size of modern day New York yet being given similar importance in the plot as species with multiple billions and massive colonial empires. Either individual quarians are literally 500x more efficient and resourceful on a per capita basis, or everyone else is lazy and stupid or just doesn't try.
Master Race status isn't "so called", it is scientific fact. If you wish to dispute this objective truth, you'll have to wait a couple weeks for my response though, as your *cough* airquotes may take a while for me to recover from. Side effect of evolving past filth and disease produced by the lesser races.
Oh, the mirth your delusions cause me.
Their role is incidental, and brought on only by the role of their superior creations (to them I mean, not superior in general), the geth and by rabid fan demand which is superior to nothing. If your precious quarians were as efficient and resourceful as you claim they would've become a true nomad species as opposed to begging for scraps from every system they come across and being summarily chased out of said systems in a manner that would be comical if it wasn't so pathetic.
I honestly wasn't even going to bring up your pitiful immune system which even the aliens from War of the Worlds are chortling at. Let's just say that compensating with tech for inherent weakness, isn't strength, it's just that, compensation. Especially since since they fail at even that, as third-graders with safety scissors are a lethal threat, nay natural predator to suit rats. And you even uttering the world "evolution" makes me chortle and choke on my superior levo-amino beverage as the inferior quarian scum don't even know the meaning of the word. Every other race, with the possible exception of asari has earned their place though millions of years and countless generations of natural selection while you sat it out on your no-insect easy mode planet. Darwin is rolling in his grave at the thought of a race that can be killed by fruit flies even still existing, let alone challenging anyone for supremacy.
Also your faces are stock models. 