The only successful plan is an Orion-like ship.
It also fully discusses the social ramifications when the entire population learns the Earth is toast and only about 10,000 of them will get a ticket off the planet.
I think I’ve seen that. It counts down from discovery of impending doom to the ship finally leaving.
There was a 1951 SciFi movie called “When Worlds Collide” that addressed that exactly. It was pretty good, but obviously dated. Good candidate for a remake.
https://www.youtube.com/watch?v=voW0RiNTbGI
Needless to say, there was engine failure when the first pulse om AM didn't fire correctly and the computer sent another, thereby overloading the engine and causing a massive AM explosion ... I suppose an AM engine was used to mollify the greenies in the audience.
Stupid idea - something one would expect from NG; more risky than an Orion and far more difficult to actually make as AM is still in the theoretical stage, while Orions could be built quickly today.
Orion ships are launched by conventional propulsion until well above Earth's atmosphere - only then does the ship begin using its tiny nuclear charges.
Here's what a real Orion mission might look like in our system:
Mars, Phobos, Demos Mission Launch: 2/28/1969.
Land Mars (Lander 1) 6/27/1969;
Mars Assent (Lander 1) 7/26/1969;
Land (Lander 2) Phobos 7/20/1969;
Phobos Assent (Lander 2) 7/26/1969;
Demos Flyby 7/28/1969;
Earth Return 4/04/1970.
https://www.youtube.com/watch?v=DSK_mymJvkM
Unlike other variations of ship propulsion, Orions can be built any size, but the bigger the ship, the better the ship works. A ship built for a crew of thousands would work better than one built for a crew of hundreds. Massive amounts of water aboard provide shielding from radiation, steering propulsion, unlimited and unrestricted usage of water for crew. Since I haven't seen "Ascension" (and the trailer does not show the aft end of the ship) I cannot say if it is a true Orion, or some Syfy variant. Looks more like a human interest show, rather than a true mission to explore or even 'save' humanity and as such has little credibility.