I don't particularly care for the wormhole method. Assuming that the leak is true, and we are in fact headed to Andromeda for the new title, I would prefer the refugees to travel to the new galaxy via a sleeper ship; crossing the intergalactic void via 'conventional FTL' means. A portal that links directly to Andromeda suddenly showing up right when the Reapers begin to encroach on the Milky Way is just way too much of a contrivance for me.
Instant teleportation to the new setting would certainly be easier to write, but in addition to feeling like a complete cop out, it would also forgo any intriguing story elements that will most certainly happen in a direct journey. Just plopping the PC and the other races into the Helius Cluster ignores any possible character growth that would happen in a centuries long trip. As some others have said in other topics about the subject, just magically zipping over to Andromeda won't feel as 'earned' as a group of refugees that banded together and made the long, arduous transition the hard way. In a conventional journey you would see a change in each race's respective cultures; you could see old resentments fade away, and new rivalries take their place, you could see a shift in perspectives as the isolated nature of the ark ship would force the species to re-evaluate their role in things. Would the Asari still be the diplomatic leaders of the rag-tag survivors after spending hundreds of years together with the shorter lived species? Would the Krogan, still maintain their aggressive nature when dealing with the cramped conditions for so long? Etc. If we just instantly make it to Andromeda we won't see any of that development, the Asari will still be the Asari as they go and colonize new planets, the Krogan will still be the gruff warrior race, etc.
As far as the ship goes, why construct a massive Ark, or a fleet of smaller ark ships when an asteroid would accomplish the same exact thing with far fewer resources. There is no need to build a ship that can house all of the refugees of the Milky Way, a large asteroid would be able to accommodate them easily. There is no need for the galaxy to scrounge for precious Ezo reserves when an Ezo rich asteroid, similar to Omega, would come pre-supplied the the necessary fuel for the journey. There would be no need to construct an elaborate discharge system for the static build up of the engines, as the rocky exterior of the asteroid could provide a perfect spot for grounding the current safely away from the living quarters. Just take some conventional engines, strap them on an Ezo rich asteroid, hollow out a small portion for the crew and blast off for Andromeda. As the refugees begin to use up the Ezo they can turn that space into more living, hydroponic or storage sections, making the vessel extremely effective at resource management.
Assuming that an asteroid comparable in size to Omega is used, and it can travel at the standard speed of 12 light years per day, it would take the inhabitants 570 - 571 years to cross the 2.5 million light year gap between the Milky Way and Andromeda, easily within an Asari, or Krogan's lifetime, and more than enough fuel since all of the Ezo would be used for the ark ship instead of supplying the Terminus systems.