The only three things that have seemed important to me at the beginning:

Immediately buy a factory on every new planet with no buildings and then start building another. That will get your production going.

Spam colonization ships like it's going out of style. You want to grab as many planets as you can as fast as you can.

Nab as many of the anomolies as possible. They're essentially GC2's version of Civ goodie huts.