I tend to play on large or bigger maps, with hospitable systems being common, and systems found in tight clusters. I now play against all bright opponents, but after my latest game im going to try intelligent/genius.
For my starting strategy I try not to rush buy anything. I find that the lease cost hammers my economy for the next 100 turns and isnt worth the sacrifice. Instead, I stick spending on max, leave tax rate at 33% and put the slider full on military.
My reasoning for this is that I can churn out colony ships 1 every 3 turns on earth, and with the first ship, I send it out with about 6mill colonists. This colony ship must go to the best planet you can find nearby, as this planet will also be a colony ship producer.
Tax rate is left at 33%, as this encourages really fast growth due to high morale, and I find that with max spending my 1000 credits starting cash will usually last me until the colony rush is done.
I send my first colony ship and my survey ships in opposite directions to sectors with lots of planets in. Their job is to scout out viable systems for the other colony ships, and the first colony ship I try to colonise as far away as possible, preferably near a resource if I can find one. This initial ship only has 100mill colonists, so I often put the planet it settles on to create a constructor to grab the resource.
Meanwhile, I settle the 600mil colony ship on a decent system, and then this one and earth churn out colony ships as fast as possible, dumping about 200mill colonists on each ship. Growth on the main producing planets keeps population up, and then each 200mill colony ship can then produce a 100mill colony ship when it settles on a planet, before I switch to a constructor.
By this point I should have 10+ systems, and when I have grabbed all the available ones within reach, I then colonise any secondary planets for each system.
Once I have grabbed all the nearby resources as well, then I use my initial burst of constructors to enhance production in all the sectors that have multiple planets in. By this stage I usually have a large amount of colonised planets, all the nearby resources grabbed, and im often just about to go into debt on my finances. Now I change spending to stop me going into negative money, and change the sliders to 33%/34%/33%.
I leave the sliders like this for most of the game (its the most efficient way of spending cash), unless an emergency crops up:
First war: I try to get battlehammer tech as fast as possible (or battleaxes in a pinch), so if I somehow get pulled into an early war I switch any planets close to making a constructor onto battlehammers and put military spending on max. Once I have half a dozen of those, I find they can hold their own against early enemy fleets.
Running low on cash: switch to 100% social, and build as many trade goods as possible. These things always save my economy, and I try to get as many as possible. I never try for aphrodisiacs as the minor races always grab them, but the others I can often get. If I have a minor race nearby, I will sometimes trade all the early techs with them that allows them to build the starting trade goods. When they have them all, I invade.
(with only 1 or 2 planets, minor races will always be able to out produce me on the early trade goods, as I have to divide my social production between 10+ planets).
The beauty of trade goods, is that whenever a new minor race turns up, you can trade all your trade goods with the new race as they invariably have a huge amount of starting cash (make sure you act fast though, the evil races will demand tributes from new minor races). I trade morale+ and growth+ goods with the major races, but I wont trade them diplomatic translators or the ship speed increase one.
In one game, the drengin had the event occur that split their empire in half due to planetary rebellion against evil empires. The new empire had no trade goods, and I made 15k from selling them all of mine!
Starbases upgraded to the max: change sliders to 0%/33%/67%. This way I keep social production going, but have a rush in research. Turns go extremely fast now as I dont have to assign constructors to starbases, and I concentrate on expanding through the tech tree. I usually try to get to the +10research techs as fast as I can, and once I have those, I then often tend to choose any techs that can be completed in one month. This makes research most efficient, without any excess research being wasted.
One last general note. Speed increases early in the game make a huge difference. I try to build a second survey ship on my main manufacturing planet once my initial constructor rush is done. My two survey ships then charge around the map hoovering as many anomalies as they can. By the time all the anomalies are gone, they have grabbed so many, that they are incredibly powerful, and easily capable of taking out +15 defence starbases.
As a by-product of great speed, the enemy AI also seems to know where most, if not all, of the resources are located. In my last game, I followed an AI constructor to a resource with my own constructor, then swiped it due to my increased speed!
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(with only 1 or 2 planets, minor races will always be able to out produce me on the early trade goods, as I have to divide my social production between 10+ planets).