It is too early to make definite plans for development beyond Mars, but we can list some of the options in this last step. These are approximately in order of distance and difficulty, but there is no requirement to do them in any particular order.
Main Belt AsteroidsEdit
Development of the Main Belt between Mars and Jupiter is an extension of development in the Near Earth and Earth/Mars transfer regions. Because all three regions have a range of eccentricities and inclinations there is no distinct boundary between them, but we arbitrarily assign the area between Mars and Jupiter as the Main Belt, and Jupiter's orbit and beyond as the Outer Solar System region.
The largest Main Belt object is the dwarf planet 1 Ceres. Equatorial orbit velocity is 359 m/s, and equatorial rotation velocity is 94 m/s. Thus to reach orbit requires 265 m/s net. This velocity can be reached by a mild steel centrifuge and easily by any advanced material. Therefore cargo delivery from any other Main Belt asteroid, all of which are smaller than Ceres, does not require any rocket propulsion. A 1.0 gravity Skyhook would be 7 km in radius and allow crew and equipment to be landed and take off at low acceleration, and a cost of 0.5% of net mass flow in reaction mass to maintain orbit.
For smaller asteroids staying on the surface will be more of a problem than getting on and off. For example, the 35th largest asteroid by diameter is 9 Metis, which has an equatorial radius of 170 km and a mass of 1.47 x 10^19 kg. This gives a surface gravity of 0.034 m/s^2 (0.34% of Earth). The rotation period is 5.08 hours, which give a rotation velocity of 58.4 m/s and a centrifugal acceleration at the equator of 0.020 m/s^2. So the net apparent gravity is only 0.014 m/s. Indeed, the orbital velocity is 76.0 m/s, so it only takes 17.6 m/s ( 39 mph ) added velocity to reach orbit. Therefore humans or low speed machinery can toss things into orbit, and a firm anchoring method will be needed to not do it accidentally.
Outer Moons and Minor PlanetsEdit
Oort Cloud and BeyondEdit
People assume that a "starship" will be a metal can with big engines on the back. Imagine colonizing a long period comet, one of the ones that came from the Oort cloud, and is heading back out there. Comets are made of a mix of ices (water, methane, ammonia, CO2, etc) and rocky materials. If there is not enough metals, get one of the metallic asteroids to match orbits with it. Then build your colony out of the materials there. Comets range in size up to 50 km in diameter, so there is plenty of stuff to build with.
The Oort cloud is many times the distance of the Earth from the Sun, and the velocity needed to get the comet to leave the Sun and head for another star is very small. All the ices have some amount of hydrogen, and thus deuterium, which means if you know how to build fusion reactors, you have power for a long long time. It will be a long trip, but you have a whole city worth of space to play in, with occasional side trips to other comets in the Oort cloud.
There are an estimated trillion comets out there, some will be along your route, more or less. The average spacing is something like 6 AU, about the distance to Jupiter. So you can in theory seed other comets as you pass by with new colonies. If some people feel like it, they could head back to the Sun, the velocities are low enough to do that.
The requirements for this kind of slow star travel are fusion power, and knowing how to build permanent habitats in space.