Lets use a NASA method. Start with the final goal and work backwards.
I see the final goal of an arcology with hundreds of thousands.
Is it on a space body for easier resource gathering or will our drone fleet [another discussion] travel? Propulsion?
Hydroponics and food? A control centre will be essential. [brackets are possible processes below]
Can we see development of salvage processes to the degree that our used [tons] of debris can be collected from smallest [particle collectors used] to largest [solar sail orbit stabilization/movement] ? In not using the usual suspects [rockets defying gravity] we can keep it cheap and possibly faster.
Research examples; Tracking needs to be developed such that we can actually do the processes above [being worked on, various salvage projects and asteroid tracking around the world, different nations, use the web to access ideas] as does the propulsion systems, drones, etc [see web, much info on development of these]. More research on medical changes in humans in space. (DNA telomeres elongate, why?)
Acceptance of the Nation among the nations of Earth would go a long way to getting us help so we can help them.
Getting ourselves organized will have to occur sooner than later
More volunteers of new ideas for the above processes, some economy [ebay type or e store]
Ratify the Constitution then vote on amendments [process currently in play]
My reply to your post is complete, please go up for the processes I outline, they are however not exhaustive, but an outline. Thanks