At the start build one Military and one Civilian research lab. Upgrade to build LRM and do the double upgrade of homeworld size in Civilian. If it wasn't done at the start do the fourth upgrade to your home world. Build LRM until you've maxed out your fleet cap. Keep your egg and LRM together with coordinated jumps so the egg gets targeted by a planets defense ships so you don't lose the LRM.
I usually destroy my cap ship factory to give me room for another Civilian research lab at the home world. With the second civlian research lab you can get Fire & Ice colony as well as upgrade the metal/crystal income twice.
Build two Military research labs on the asteroid (after upgrading the asteroid) and research the carrier. Upgrade your fleet cap and start building carriers until you get to your second fleet cap. At this point I also like to start upgrading missile tech which boosts both LRM and fighters (don't build bombers).
Build a Civilian lab then research the metal/crystal income twice again.
Build another Civilian lab then research the trade port and put up at least one trade port up on all worlds.
Research the media hubs and put the hubs up at strategic spots in your systems to get all worlds that 10% bonus.
Research Enslaved Labor and Salvage tech on Civilian.
Build two more military labs to get your cruisers producing. Continue upgrading fleet tech and military tech.
At some point build the Skirantra Carrier as your second cap ship and max out it's repair ability.
Once the Egg gets to level 6 you should be able to blast any world without needing bombardment frigates.