So, lots of good advise above. Here is what I do.
Turn one: I purchase a factory on HW and set to build (1) Lab, (2) Economy building, (3) Moral boost. I then set the Production slider to 100%. I set Military/Social/Research slider to 20/20/60. I set Taxes so that moral is 100%. I create a separate Colony ship that is a freighter hull with TWO colony modules plus life support. I convert the miner into the new colony ship you just created. I set the Star Base on HW to producing colony ship
Set focus on Social building on HW. Then I dock the current Colony ship to HW to pick up the remainder of the 250 colonists, launch it again and send it towards the nearest star cluster. Also I send the Flag ship off in a different direction. Then hit turn.
The next couple of turns I pretty much explore, looking for other planets to colonize. I won’t boor you with details but essentially I set up colonies with only one econ building (unless I hit on a high PQ planet that I plan on using as my Econ Capital). I also put up recruiting centers as soon as I get them to boost populations and minor income boost. These buildings can all be bulldozed over once you have good economy going and replaced with whatever you eventually need. And keep an eye on your Social building. If your planets aren’t building anything at all, shift your slider so that you put more into Military. Personally I don’t ever change my Research slider unless I am REALLY hurting for research, or BC.
I manage the moral to as close to 100% as I can until I get down to my last 700 BC. If I have to let it slide, I don’t let it slide beyond 85%. Keep in mind that the higher your approval rating is, the more your people proliferate. But it is at the planet level, so if your moral dips due to over-crowding on the HW, so long as the colonies are happy (100%) that is OK (in my book). Also, don’t be afraid to drop your production in stead of increasing your taxes.
I keep focus on HW to Social until all tiles are built except the Moral, and then switch to Military. Have your HW build as many colony ships as you can and send them out immediately. Have any new colonies build scouts to explore your horizon. Also, Freighters with Survey (Sensors I) modules and life support will help you mop up some of the anomalies around. And if you end up with extra colony ships and no immediately colonizable planets, use the ships to ferry colonists to your new colonies. This will help lower the over-crowding on HW and boost your econ on the colony worlds.
I focus on the early techs that give me Global bonuses (Planetary Improvement (+10 Military/social/research) that kind of thing and Econ stuff. But tailor that against research needs as well. Also, the sooner you can get to Trade the better. This tech gives you a plus to diplomacy and allows you to set up trade with the neighbors. The money isn’t a lot, but should be enough to get you green before you hit higher income methods. Also, it allows you to play nice with the neighborhood kids (build up Diplomacy with other races).
Don’t colonize low PQ planets in your turf unless there are no other better choices. Let the PQ4 in your home system sit. Sooner or later a Civ will colonize it for you and then the influence will flip it to your Civ. Keep your colonies more or less in bunches. Keep your eye on a frontier of sorts. The more spread out you are, the more enemies can simply pick off. But also keep an eye out for strategic “jumping off” points that will allow you to build up on your enemies front door step without upsetting them.
Once you are in the green, then you can start building up the other worlds. As a general rule, I don’t force purchase anything except the initial factory. And I don’t purchase on credit at all. It is just plain a burden on your early economy that you don’t want to deal with. Also, consider putting some BC right away into Espionage. In the first 30 or so rounds you won’t miss the extra (because you will be negative no matter what you do) and it will help you plan for it in the future.
As far as farms are concerned, I never build more than one on a planet, and never on a bonus tile. Pretty much, you want to keep your population below 16 on any given world, and then only on your econ worlds. Higher populations might sound like a great idea on paper, but the higher your population, the more your Moral takes a (major) hit.
One final thing, know your race strengths. If you are playing the Drengin or Korath or some other high military race, strike early and often. Grab planetary invasion as soon as you can and take from your opponents before they can research up to your soldiering level. In fact, I would recommend this even over colonization because you get free techs out of every invasion (provided tech stealing is on and your enemy has tech you haven’t researched). If you are playing more diplomatic races, don’t ignore your military. You may not be good in a fight, but your opponent will think twice if you out ship them. And your military might gives you a boost to your diplomacy.