You'll find that it's much more efficient to get new planets at the start then to maximize production of ones you already own. Adding slots for Civic/Military structures should be saved for when you have 8 or nine planets/'roids. The only thing that you should upgrade as soon as you take a planet is the population cap for the planet. If you don't do this, it's an economic drain...
A standard start has been around many times :
3 scouts,
cap factory ( then cap, Marza for myself, but some prefer a colonizer ),
a crystal extractor,
then the two metal extractors,
as many cobalts as possible.
While these are queued and depending on what the scouts report, take the nearest 'roid.
For myself, I put up two civic research structures, research fire/ice ( dending on what's in my area.. ). Start grabbing planets. After that, it's up to your style. Some SPAM LRM's.. some rush for HC's.. some go for an Econ Boom.. others turtle ( and die ) ..
Expansion is key. More is ALWAYS better. The fleet should be your first, second, third, and last thought.. if you aren't riding your fleet cap, or sweating how to raise it, there is something wrong. Five fully maxed planets with a single cap and 10 cobalts to defend them all will be obliterated by the raving hordes that will pour over your borders from an empire that has 15 mediocre planets. Fleet first.
When the game hits the midway point, there are no more free planets, and you have an economy, THEN you upgrade to trade ports, broadcast centers, and production buffs so you can afford to raise your fleet cap... or pay for the one you already have.