Mary Sue: Mary, meet Lazarus Long. He's immortal and can kick your ass and he's got fiery red hair.
Mary Suetopia: A more downplayed version. Technology has gotten to the point where inhabiting a new planet is as easy as living in a big city, and given that the family did decide to immigrate to the new planet, they do get to settle how they want. It is indeed unrealistically peaceful and efficient, but it did have to take advtange of a whole new planet and technology to make it work.