The driving force for colonization will be to access some sort of valuable resources for the colonists to use. Most of the needs of the colonists can be broken into broad categories:
- Energy, to allow them to do all their other activities
- Water, to support life
- Elements like Carbon, Hydrogen, Oxygen and Nitrogen in
order to support life
- Metals and rock for construction and shielding
Luckily, modern space research has allowed us to discover that most of what we need is relatively close at hand. The Moon is the first place we'll go because it is quite close and has everything in categories 1,2 and 4. It is convenient to develop and refine techniques before taking the next big jump.
The next easily available source of valuable resources is the NEO's (Near Earth Objects). These are much smaller and easier in terms of deltaV to reach than even the Moon, and collectively have all the major categories in abundance. Being very small, mining and accessing the resources requires that you learn how to operate in microgravity environments, but this experience will lay the foundations for moving to the asteroid belt, the Jovian Trojans and even (in the distant future) the Oort cloud.
Unlike many space enthusiasts, I would actually give Mars a pass. As a planet it is too small to maintain a thick atmosphere, but large enough for gravity to become an issue with launching and so on. Energy is also an issue, since Mars is far enough from the Sum to make solar panels less efficient, so you would have to haul nuclear reactors there.
The next major nexus of colonization will be Jupiter. The Jovian system has all the categories in abundance, with a powerful magnetosphere which can be mined for energy and 67 moons orbiting the planet itself. Europa alone has 3X the water as all the Earth's oceans combined. Because of the tremendous concentration of resources, it is entirely plausible that Jupiter becomes a civilization or nation on its own, a polity independent of Earth and quite capable of standing on its own.
I can see a fork happening at this point in the timeline. Some projects like building giant lightsails for space development and interstellar flight, creating antimatter as a compact energy storage medium and so on will require settling Mercury. Mercury is very abundant in category 1 and 4, and will have to import its water and life supporting elements. In return, gigantic lasers can be used to beam power to deep space targets far beyond the limits where solar energy would be useful.
Deep space colonies in Saturn would mostly be focused on the moon Titan, which has a thick nitrogen atmosphere, and the planet Uranus, which has the gravity field and radiation environment which allows for atmospheric mining, especially of 3He, which would be a valuable fuel for deep space colonies and spacecraft. Settling beyond might actually be a race between rising populations needing room and the building of a Dyson swarm around the Sun to harvest energy and create living space for trillions of sentient beings.
You can see in a setting like this here will be a multitude of opportunities for trade (not every place haas all th elements needed for successful colonization), as well as some fairly well defined "zones" for separate cultures and civilizations to develop. From Mercury to the Asteroid belt will probably be the "Solar" zone, where cheap solar energy is the economic driver. Jupiter will be its own zone for the reasons described above. Deep space will be its own zone because of distance and the need to either import energy from Mercury or mine 3He from the atmosphere of Uranus.