Question, since the game is so new I'm still very confused about the pace early on. Maybe I'm just being bad about efficiently constructing resource collectors, but it seems to take a very long time to get the ball rolling. How long does it usually take for you peeps to get planet #2?
No matter who you start as, there will be two planets suited for your race within very close range. As soon as you get colony ships (which should be the first society tech you go for), send one out to the closest one. Yeah, you'll probably go into the negatives in energy while it builds up, but you should've saved up a bit by then because there's no much to spend energy on until you start expanding. So it should only really take as long as researching colony ships and building one does, which isn't too long in the grand scheme of things. Getting minerals for it is slow at first, but while the tech is researching, plop down some mining stations in your home system to get a flow of at least a few energy credits and at least 5 but preferably 10 minerals, and when you see the tech is close to finishing, save up and splurge on it when it's done. Then use the minerals that build up over its build time to finish setting up the mines in your home system and any others withing your borders at that point.
This whole time you should have your science ship surveying systems. I've only played with wormhole so far, so I try to hit up all the ones in the first ring as soon as possible. Don't build a second science ship or constructor until you get your second planet, and build a science ship before a constructor. Science ships are good ways to get a boost in the early game by finding anomalies and whatnot, and they'll also give you a clear idea of where you should expand to and where you should build frontier outposts to grab some good shit. Make sure your science ships have scientists in them, and try to grab ones with traits relating to either survey speed or anomaly chance. If you get any maniacal ones, set them to be research scientists, it's worth it.
Oh, and make sure you set up governors for your first two planets, you won't need an admiral at that point so you can use your leader slots to eke every bit of productivity out of your planets as possible.
Ninja Edit: Yeah, full scale bombardment is lame. I don't get why it's a policy at all, I bombarded a planet for a year or so while I was waiting for my ground forces to finish leapfrogging their way there, and nothing really happened to the planet - no buildings destroyed, no pops dead. Keep in mind this is a 30k power fleet, so they've got a decent amount of firepower. I was expecting to glass the planet and all I did was make everyone unemployed.
EDIT2: With that said, the planetary side of war is lame as fuck. It feels so barebones, I'm sure there'll be a DLC focusing on it. Why can't I do anything with the planets after I've occupied them? I've got a massive fleet hovering around and I've filled the slots on the planet full of xenomorph troopers, I'm a maniacal xenophobic miltaristic empire whose sole goal is to enslave or purge everyone, and for some reason I can't touch the buildings or the people on this planet I've taken? I want to be able to sic my army on the populace, purge them all or enslave them all and ship them off to some far flung colony, do some actual damage to my opponent. But the military aspects of this game feel very poorly thought out and designed for multiplayer only, so I'm not too surprised.