I am basing these options on the 'Ark departs before arrival of the Reapers, or at the least before Crucible is used' premise. This is due to the fact that my understanding of ME:A is to partly not set the cannon ending for ME3 while preserving largely recognizable technology of ME universe.
Slower than light drive. Cryogenic stasis or v~c for time dilation.
Note: Allows for things like arriving to Andromeda to find that Milky Way galaxy survived (in any state), progressed, developed FTL drive, arrived to Andromeda and went extinct/was destroyed all during the Arks travel time.
Direct Reaper salvage
Note: Unlikely as indoctrination from directly salvaged drive will be the main concern.
Direct Collector salvage
Note: More likely than Reaper drive in both the availability (multiple black ships were hinted on), the fact that salvage would happen around the time Shepard offed the Collector Base, giving time to integrate it in a ship, and the lack of shown indoctrination effects.
Reverse engineer of Reaper drive.
Note: Runs in the same issue as integrating the drive directly. Even dead reapers can indoctrinate the organics, so working on studying the drive in sufficient detail (remote probes are likely insufficient for studying extremely massive complicated piece of technology) in sufficient time frame is unlikely.
Reverse engineer of collector drive.
Note: This could be possible REing a collector ship drive (captured roughly at the time of the destruction of collector's base) would allow pouring resources into this project before the arrival of Reapers and thus would not interfere with Crucible construction. Ship captured - drive studied - potential for deep space exploration/emergency escape noted - model for drive technology created - prototype created - Reapers arrive - prototype used for Ark. Last few steps can be shuffled depending on personal preference.
Old Tech:
Note: Liara can always find some more tech in Mars archive! Or Leviathans could give humans drive tech just to get rid of them. Or Javik could remember some tech cache location. This is one of those all too used devices that I am sure BW can come use to explain anything, and likely not very gracefully.
New Tech:
Note: Can always discover some non-mass effect model and use it to break out of Reaper's tech cycle. But this is actually a lot harder than people realize. There is a LOT of inertia in thinking. Its not simply 'oh, now that we know that there other technological advancement paths outside of mass effect fields, let me go develop FTL drive, be back in 10 minutes'. The process would be slow and a lot of much simpler devices would need to be developed on the way.