Your first cap ship is free and can clear your starting astroid by itself, so you want to get your cap ship factory first. Thats what I do anyway, I just set it to build right next to my builder ships so it doesn't have to move very far to start it. Then I queue up the crystal extractor and the two metals, in that order because I always need crystal more. The sooner you get those up the more resources your going to be getting, in fact I don't think you start out with any metal/crystal income untill those get built. So build them quick(obviously).
After your first cap ship is done I recommend just skuttling the factory. Its taking up 4 logistics and lets be honest, your probably not going to be getting another cap ship for a while. If your rich enough to afford paying for the research, spending 3000 credits on a single ship, and losing 50(?) fleet cap, then you can probably afford to re-build a cap ship factory to. Not to mention skuttling it gets you just a little more resources, and frees up 4 more logistics for trade centers or what have you.
While all this is happening you should of course have built several scouts, 2 atleast, sometimes I'll do 3. Your cap ship is off clearing your astroid so build a colony ship after the scouts so you can go colonize it. Now you've got 3 scouts, plenty of logistics, a cap ship, and some starting income. Where you go from there is your own choice.
Remember to upgrade infrastructure on your planets as soon as possible. I'll even do it before building extractors sometimes. Sorry to the guy I played with the other day if you read this, but you make a good example here. The guy had 5 planets and was relying on a "strong economy for producing capital ships with support cruisers" for winning the game. About, I don't know, an hour in, he had maybe 20 ships making up his entire fleet. I asked him what he was doing(we were on a team ...) and thats when I heard of his plan. He'd just been building up trade centers, I asked him where all his money went(he couldn't outbid a guy on the priates, he only had to put up 1250 credits, he was TEC) and he said "research." I'm getting off track, the point is none of his planets had upgraded infrastructure(he'd forgotten that red=negative). So all of his planets were losing him money. Lets put it this way, before I got defeated by the other guy I had 3.3 income a second coming in. I was 2nd in credit income, the other guy was first, this non-infrastructure guy was last(yes, it was a 2v1. Considering my ally though, I like to think of it as a 1v1). So despite having 5 planets and trade centers, he had less than 3.3 income a second. This was his form of building a "strong economy." He hadn't even been attacked yet so it wasn't as if he was losing ships and having to rebuild a lot of them.
So upgrade infrastructure, its important. It takes 1 upgrade on astroids and 2 upgrades on everything else to bring in more income. Population is also a good mean sof making money. I think last time I did a test it was every... 30-50 population was another 1 income a second. Keep that in mind when your getting population upgrades or getting the third rank of infrastructure.
Hmm, also remember to build a fleet. If your not researching something you should be getting light frigates and long range ships(I've only ever played as the Vasari). How many of each depends on you. Remember to send your cap ship to planets first so that the militia fires on them. They are big and can take a lot more hits than the smaller ships. Just send them in, let them fly around for 30-60 seconds so that the miltia are all firing on it, then bring in your other ships. Don't worry, you cap ship probably won't even lose its shields, if it does just run it away. Also retreat wounded ships, every ship you save from the militia is a ship that you don't have to rebuild and can fight the enemy. I ussually hit retreat when they lose their shields, maybe even sooner if they are being attacked from a lot of ships(or heavy cruisers). The ships will go to follow the fleeing ship giving your ships more time to do damage without really taking any themselves(the enemy is busy shooting that ship which is going to phase jump out anyway).
Edit -- Also don't be afraid to buy crystal if you need it. Crystal income is ussually low in the begining before you get a ice planet or something, so if you need that crystal for upgrading infrastructure don't just sit there letting it trickle in at .51 a second. Spend some credits and buy it. Your probably getting around 13-15 credits a second, but only .5 crystal a second. You'll get those credits back quick enough and the time saved from waiting for crystal to build up could be very important.
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Alright though, thanks for the help bro.