I think Mars was chosen for these reasons:
- Despite Venus being closer to us and being much larger than Mars, it is also the hottest planet in the solar system. So we can't think about colonising it just yet.
- That leaves the second nearest planet which is Mars.
- Existence of water in frozen form.
- It has a similar day (24.5 hours) as Earth and there are seasons over there too.
- Scientists think that they can terraform it and turn it much similar to Earth.
- Plants can grow in Martian soil.
- Since it as a lower gravity, it could become a pitstop or a stepping stone for further colonisation like Jupiter's moon(s) or Saturn's moon(s).
For why we should believe Stephen Hawking completely, we should not, but he is not the smartest person on Earth for nothing and his predictions have some weight, or at least a lot of people think so.
About worrying about things we can't control - True, but we can control things to a certain degree and each year, technology helps us to expand our control to the point that we can create a second Earth for ourselves and ensure the survival of humanity. Not just this generation but several generations to come in the future.