The Serenity movie may take a different position on the galactic venue but I agree that the producer are a bit confused or uncomfortable with the where and how of it all. In spite of the comment regarding finding a new solar system, in different episodes this is called into question with contradicting statements.

Cult fans that choose the solar system version have speculated on sub-light ships in an exodus from Earth. They have even gone so far as to figure what stars are in less than generations range and what star types might be likely to have lots of planets and moons.

It doesn't pay to think much about it because it invariably falls flat.