When do you start building combat craft?
I build a small fleet of armor destroyers right away just in case I get hit with asteroids or something.
When do you start going against planetary defenses like the swarm?
For Swarm I'll usually hit them once I have PD tech and UV lasers. With a good fleet of PD destroyers and UV-armed armors you can take out a swarm hive.
How do you equip your main combat craft?
Depends entirely on what my enemy is doing and what techs I roll. If possible my ideal destroyer fit is AI fire control, armor mission section and antimatter drive with antimatter cannons in the medium slots and a mix of pulse phasers and PD phasers in the smalls. You have to be flexible in this game, you may not even get some or any of those techs.
Is there any way to take over planets or do you just bomb them to death?
When you bombard a planet you will kill the imperial population off first and the game will ask if you want to continue bombarding and kill the civilians too. If you leave the civilians alive you can recolonize the planet and have the established civilian population join your empire.
Be warned: If you do this before you have habitation tech for that race and you start terraforming the planet away from that race's ideal, you will start killing them by the millions.
I had a decent game going, but I think I slacked too much on aircraft upgrades. I was wining the war with my purple lasers until they came at me with heavy emitters.
Emitters are devastating to close-packed formations and destroyer swarms but less useful against cruisers/dreads and absolutely shit at bombarding planets. If you roll energy absorber tech or EM shielding tech (EM shielding is above the 2nd reflective coating tech) then that will cut emitter damage by a lot. Emitters iirc aren't very good against shields either.