I would add a third and fourth and fifth possibility.
3. People, inspired by the possibility of freeing themselves from war, oppression, climate change, religion, etc will see Mars as a new frontier where they can set up a more rational society, and travel there to build colonies in much the same way as the many Utopian projects in the United States were originally set up.
4. People, inspired by the possibility of becoming extremely powerful by setting up their own little kingdom, will travel to mars and build colonies, and put themselves and their friends on top. Eventually, the people they put on the bottom will rebel.
5. The most likely possibility, though, is a combination of 1, 2, 3, and 4. Mars is a big planet, there's enough space to have penal colonies, settlers, utopians, and power hungry crazies.