How much energy would be needed to move the sun?

Somewhat of a stoner hypothetical physicist question and not a pure pragmatic science question - but let's say future scientists somehow detect there is some impending hazard on our solar system. Maybe it's a collision with another star, maybe it's some kind of cosmic radiation - I don't know.

1. How much energy would be required to physically move the sun X light years away from that hazard? And how can that function be described in terms of the energy actually generated by the sun itself over time?
2. If there was some impending hypothetical disaster, would it make more quantifiable sense for future humanity to move the sun X distance away from that disaster or would it just be better to move all of humanity of mass Y distance Z to another habitable planet somewhere in the habitable zone of the galaxy?

Edit: I am asking question (2) because I am assuming that humanity would need to travel there at a really fast speed if it was a radiation event, and that the sun shields a decent amount of cosmic radiation if you push it far enough away. Maybe in situation Y we would have to go close to the speed of light (taking huge amounts of energy) for cosmic radiation, but slower for a collision event.