Ok, I play at crippling level, so spoilers follow... if you do this, you will pawn your opponents at normal or intelligent.
Turn 1: I purchase outright a factory on my home world, purchase outright a speed 3 colony ship on my home world (you can create this once in ship editor, then it will be available for all future games). Set taxes at a level that gives me > 50% approval (this is for 1.0.X). Give full funding to research (0 to social or military production), and increase the spending slider to 100%. Auto-explore scout, send first colony ship to a "close" star system (since it is slow). Set to research propulsion, which will finish in one turn, if you have done everything else as listed.
Turn 2: Start building second factory on home world (normally this time), purchase outright a speed 4 colony ship with no range modules. Send my newly build spd 3 colony to a system that might be long-range but that I want to beat the computer to. Change funding 100% to social production.
Turn 3: Your factory is nearly complete on home world, adjust spending sliders between social prod and research to be the minimum to finish factory in a single turn. Start researching xeno research. Purchase either a spd 3 or spd 4 colony ship depending on how much range you think it will need. Send off your new colony ship.
Afterwards: Switch production 100% to military. Assuming you need more colony ships, keep building them on homeworld, if not sure, build a spd 3 constructor, to claim any resources you have found. No more purchasing except if I find a world with a production bonus, I will rush-build a factory there for the first turn. Once I colonize a world or two, switch spending to no military, split between social and research, and then "focus" military on your homeworld. On every other world, I build two factories first (unless it is PQ < 8, in which case it gets one factory, or it's PQ >= 14 where it will get at least three), then starport, then research and entertainment, then market, then farm. I don't actually set military spending above 0 (just focus it where I need to build things, like home world, or any production powerhouses) until all initial colonies have starports.
I don't build scouts --- let your colony ships be scouts. Oh, by the way, I like to spend 3 points of racial picks to get +4 sensors.... you will be amazed at the advantages this gives --- you can beat the computer to nearby worlds, and later on, you can see when he is trying to invade (zooming out to the long view between turns is especially useful here --- his fleets and transports jump out at you).