>>14249190With nothing better than chemical propulsion, if we can colonize Mars, then the time scale to colonizing the entire solar system including scattered disc objects beyond the Kuiper belt is <1000 years. All of those objects are within colonization range via chemical rockets of one or more neighboring objects, so if we can make one colonization step wave per 100 years we will be ten steps out in 1000 years which puts everything in range (by that I mean, step one is the Moon and Mars, step two is Jupiter and the asteroid belt and the trojan group asteroids, step three is the Saturnine system, step four is Uranus, step 5 is Neptune, and step 6 thru 10 is progressively father out into the Kuiper belt, where distances are large but delta V requirements are smaller).
Colonizing the solar system requires a gradual improvement in contained life support systems and the ability to take all waste products, slag them with heat into granular glasslike particles, leech the elements in that slag back out into usefully pure form, then use that material as feedstock for new products (actually a fairly simple technology, we just don't do it on Earth because our energy is too expensive and raw materials are too cheap).
Without launch constraints, building very large habitats is like building highways and bridges and skyscrapers on Earth, but easier because it's zero G. Colonization of the asteroid belt will require the invention of very large habitats with the recycling tech I described. With those habitats, and a sufficient number of them (allowed by just extending timelines and letting birth rates do their thing), you can do interstellar colonization fleets of thousands of ships each containing dozens of square kilometers of internal living space, which all leave roughly at once and stay in a loose cloud formation on their thousand year trip, trading with one another and breaking down and rebuilding aging habitats as they go.