Your flagship is what you need to use anomalies. You can build other survey ships later, but at the beginning only your flagship can use them.

For asteroids, you start with an asteroid miner, and can build new ones from the start. These boost production on whatever planet is on the receiving end of their output.

The resource points found randomly around the galaxy are what you build mining starbases on. Send a constructor ship to these, then additional constructor ships to add additional modules on the base.