[Gryphin]

I believe Fyron, tesco, and Rollo showed me how to expand.
Turns 1 through 5
Home worlds use Emergency Build to build Base Space Yards
The Base Space Yards are then set to Emergency Build colony ships.
by Turn 5 you have researched Propulsion III, and either Research II or Ship Yard II or ....

If I have researched Research then I upgrade my Research Facs on Emergency build.
If I researched Ship Yards I end Emergency build
Upgrade Planet shipyards and Base Space Yards when as the ques empty.

You have to watch your resources very closely or you will most likely run out of Rads and maybe Mins.

Note: I only play against the AI these days. There are a lot of variables here.