Might as well chime in:
Flagship to autoexpore, colony ship headed twards something decently promising.
Buy a sensor ship immediately and send it out scouting, on large galaxies, buy two. Possibly buy a colony ship if I find a good world and its near a neighbor or if I find a 2500bc anomaly.
Buy a factory. On higher difficulties, make that buy a factory on some sort of manufacturing tile or else restart the game. Even the min manufacturing bonus can shave several turns off at the start.
Tax to 49% (or 59% with enough morale bonus), spending to 100%. 100% social production. If I have a good manufacturing tile, make 1 factory per turn until the capital is close to filling up (2-3 free tiles). If you're feeling like micromanagement, you can adjust social spending down and military up as you complete factories, so that you don't overspend social too much. Then put the manufacturing capital in the queue but don't actually start building it, instead set Military spending to 100% and start putting out 1 fast colony ship per turn. (might or might not work, depending on racial bonuses/tech, but usually works for me as the Yor or as a custom race).
Depending on tech level, buy a factory for each new colony if possible (tends to vary based on how many cash anomalies I get). Specialize social spending. Build 1-2 factories, and decide how to specialize the world. Large worlds are usual econ, medium worlds are usually factory worlds, and small worlds are usually research, but it varies depending on tiles and I try to keep at least one large world to stick a tech capital on. If I find a world with good manufacturing bonuses (I've been getting lucky with precursor mines lately), I'll cancel the unbuilt manufacturing capital on my homeworld and move it there, otherwise it'll complete itself when I turn social spending back on.
Starports are the third item on the list for all manufacturing worlds, but I don't bother with them for most others. If I can't decide on a planet, I make it a generalized world. 3 factories, starport, couple farms/entertainment and a couple econ buildings. Typically where I make cheaper ships and useful for extra places to buy ships in an emergency, but not optimal. I always try to have at least one starport per "cluster" of stars, so if needed I can purchase a ship at the nearest starport and move it to defend a planet the next turn.
Once you start running out of scouted colonizable worlds, set spending to 50/50 social/research and start moving up the tech tree. Specialize your homeworld on military so you still have some ships coming out, but this gives the rest of your colonies time to fill out their social buildings a bit more. Get the universal translator first, then see if the AI have any holes and try to fill them. You'll be behind on tech for a bit, but can catch up quickly once you turn it back on.
The idea behind this is to reduce purchasing ships as much as possible. You need at least one scout ship out as soon as possible so you know where to send your colony ships, but if you can avoid buying colony ships your initial 5000bc goes a lot further. 1 colony ship per turn for the first 5 turns gets you a quick 5 colonies, but that also means you don't have the cash to buy factories to get them started well. If you wait till you've built up your capital a bit, you can pump out 1 colony ship a turn for at least 10 turns, starting 5 turns in and still have cash to buy factories for at least some of the colonies. On larger galaxies, its worth giving up a few turns to pump the ships out longer.
And don't forget your military once your other factory worlds start developing. Having a decent military is key to keeping the peace and not becoming a target of opportunity for everyone else. Once you see someone else start building ships on the timeline don't ignore it for more than about 10-15 turns or you'll be in trouble at higher difficulties.
