Let's start with the asteroids
If you wanted to really get humanity into space in a big way, I would focus on two key areas:
--Space propulsion and systems for long-term spaceflight
--Developing biological methods or treatments allowing humans to live and reproduce normally in zero-G.
First part is probably easier than the second, but then I'm an engineer, not a biologist.
Do these things, and humanity can live anywhere there's sunlight and raw materials. With the right power sources, you could skip the sunlight.
Frogs have to live down in wells. Not people.