Some good advise would be to almost completely avoid building mines on your core worlds. If it's Energy/Mineral tile, Energy always comes on top. Don't neglect science, though. If you're already rich, it's okay to use the blank tiles for science.

You don't really need too many minerals, as rebuilding your fleet will take ages anyways. What you'll want to do is have Energy to maintain a very big standing force, which will lower your losses in battle on its own!
-The only exception would be in early game, if your starting systems are mineral poor. Temporarily building some extra mines to makes ends meet is good in that case, as well as moving pops from the power plants over to the mines, to have heaps of minerals to do stuff with!
Also there's Kinetic start vs Energy start. One thing that makes Kinetic better is that you might be spending plenty of Physics time doing Power Plant and Solar Panel research. Shields and Ship power, and the sensors are also in Physics. Energy weapon-focused playthroughs didn't feel too much tighter on tech, however.
Finally, I wait with the real ship spam until Engineering Bay/Crew Quarters come up. Just having any Admiral lying around leading your fleets has a chance to give you Fleet Logistician, which makes you support an even bigger doomstack! Until that, we try do only peaceful expansion, and use some Defensive pact for deterrance. Just build enough ships not to fall into Pathetic/Overwhelming so that it deters them.
Also Ordered Stratocracy/Mega Corporation are pretty crazy and push fleet size even further. A nice thing about Junta/Stratocracy is the better Admirals, which adds more maintenance discount, on top of the maintenance discount you already have.