In SP, it's always a good idea to build a few scouts early and set them on auto-explore.
I also build a capital ship factory and a crystal extractor first (since you start with 2 construction ships, these two will be built first), then the rest of the extractors.
You generally want to expand quickly so that you have more resource income, just be sure to upgrade your colonies' infrastructure quickly, otherwise they are a money drain - so just make sure you don't over expand. Crystal is your main limit in the early game, so you just need to make sure you have near enough to do the infrastructure upgrades as soon as you colonize.
Getting a good economy in SP is I would say more important early on than a military, your first capital ship is free and it can clear the militia around most neutral planets to make room for your colonies.
I always build 2 civic research stations as quickly as I can if there are ice/volcanics nearby - getting an ice planet early will help your crystal income incredibly, and will allow you to progress much faster up the research tree, they just need the 2-lab research to allow colonization.
Depending on the race you play (I recommend TEC, they easily have the best economy), getting trade ports up is also a great help, especially if you're short on ore/crystal since you can use credits to buy your resources off the black market. Vasari get trade ports much later, so it's harder to start off with them.
This is a pretty general overview, but I hope it helps a bit
