For the first turns.
Set your taxes to keep your approval at 70% or better. Adjust your spending to be barely profitable. Set your spending priorities to 40 military, 10 social, 50 research. Buy your homeworld a factory, set up a second factory as your first build (even if the first one is on a bonus tile), then layout your homeworld however. Redesign a colony ship with two engines, one support module, and no sensors. This will be less expensive than your basic version and faster to boot. Buy one, set your homeworld to build them constantly. Send your Survey ship off to find anomalies. Send your starting colony ship to the second habitable planet in your home system or a planet within one turn of your homeworld (if it exists). Set the first build item on your colony to a factory, followed by a starport, followed by another factory, then whatever. Buy the factory. Research priorities are negotiable, pick whatever suits your tastes.
End turn 1.
Turn 2.
Buy your homeworld's second factory, buy your colony's starport. Set the colony to buy colony ships. Leave it alone. You will not touch this world again until it starts producing colony ships, should be something like 15-30 weeks, depending on bonus tiles. Launch the second colony ship from your homeworld, buy one more.
Send the second ship to the nearest star system. Check your economy, make sure you're staying green.
End turn 2
Turns after 2.
Nothing really to do here, unless you want to risk buying another factory or ship (don't mess with this too much unless you get a nice cash anomaly). At this point you're clicking turn until colony ships are done, then you start pushing them out to the nearest star systems in all directions (don't get too linear, even if you see planets beyond, unless its a purple star or something special), don't worry about more than one planet per system just yet. Expansion here is ultra critical moreso than thoroughness. Keep to the pattern of the first three items. Factory, Starport, Factory. When the starport is done (you can buy these, they're fairly cheap), set them all to buy colony ships.
Keep driving the border out as fast and far as you can. If you encounter a species, use one planet's ships to fill out the systems in a direct line between you and the other race. This will prevent a lot of headaches with trying to compete with influence. Keep an eye on the map, and start filling in the outer systems when you're within a sector or two of the other's influence zones. If you see someone encroach fast, don't panic! Influence moves a lot faster than those colony ships, and it is still possible to overwhelm a border world if you're fast enough to slam the other planets around it quickly.
This opening phase requires a LOT of aggression to get down fast. Keep an eye on the Drengin, Drath and Kvorx. They tend to get heavy with their militaries fast, don't hesitate to trade tech's to keep them pacified if you encounter them and they want to get ugly. You're going to be exposed for a while, but its not something that is necessarily a bad thing if you're smart on the diplomatic front. Your high research value should have you cutting a wide swath through low level techs you can use as trade off bait for techs other races have that you want. When you start to get boxed in, trade up ship designs for Construction ships and Freighters. Trade more with races of opposite alignment. If you make them dependent on you for financial sustainance, they're less likely to risk a war with you cutting off trade.
Whatever you do, if you can avoid it, don't burden your planet's economies with a lot of ships. As your empire expands and starports come online, cut back production of ships leave the starports empty and idle and focus on the planets making them the fastest. 10 turns or less per ship. If you have a planet with low population making ships fast, then don't take more than half the colony's population or 200 people, which ever is lower, but don't turn down their production output. At this point, a planted low pop colony beats a high population colony five weeks further out.
While all this is going on, don't hesitate to turn down the expense slider to keep in the green, even if it means losing time on ship production. Once you've got 12 systems loaded up and growing with only 4 or 5 starports spitting out ships, you should start to see profits come up. Remember, you're only putting 10% into social spending. Don't level that out until the colony rush is over. Then you can reverse social and military as you see fit. After the colony rush, make a couple worlds build military vessels with whatever tech you've been able to muster up, and the rest of your worlds build constructors to start putting up influence, economy and mining starbases.
If all goes well, you should have between 15-20% of a Huge galaxy under control when the expansion is over.
