Well we are certainly going to be building on existing colonies - the whole point was to decide how much, and if we should centralize or spread out. We have the ability to not have to choose...stick these dense, defensible installations on every major one we can - a central hub (useful for shipbuilding) can wait until we have the money for it, which shouldn't be long.
Spreading out, mostly because we're limited in the amount of laboratories and factories we can construct in each.
Supporting colonies is an interesting idea though - what tech do colonies use/rely on that we can make, not just better, but cheaper?
That's somewhat complex, but as I already said, simply our Arc Reactors and Repulsors alone will have a large impact on Alliance economy, including colonization.
For starters our Arc Reactors provide large amounts of energy, while needing no fuel and very little space. One of our small ones, the 3GW ones, can probably easily provide enough power for the everyday needs of an entire habitation complex, while both saving money (no need to purchase fuel and have it shipped in) and space (meaning more other materials can be carried, instead).
The Repulsor, meanwhile, doesn't require fuel to produce thrust and produces no heat. Combined with an Arc Reactor to provide power, a ship using it can completely do away with fuel tanks and the like, and use all the freed up space to carry more cargo, passengers, etc.
Overall this means that shipping in Alliance space will become *vastly* cheaper and more efficient once we start selling ships, which includes transporting settlers, materials, equipment, etc. to new colonies.
In addition, our Legionary suits mean that an extremely small garrison can fend of *vastly* larger numbers of attacking pirates, slavers, and the like, which in turn reduces the running military costs of establishing and guarding new colonies somewhat.
And in addition to all that, if we go and develop Quantum Entanglement Communication about a decade early, it means that fairly quickly pretty much all colonies will have completely un-blockable/jammable communications with Alliance command in case of an attack.