Go into the city screen and change the planet you are building on, make the first building to construct the racial building(nutrion facility) EG Human Communities if playing the EA, as soon as you can complete the building with a 'rush' purchase. This will reduce the current research time.
Also make sure that the first research project is Advanced Computers (I'm at work so cannot verify all the information I am providing) but it's the one that enables you to build the University. As soon as this research is complete you should start rushing these buildings on all available planets.
The first stages of the game shouldn't be about getting a ship out into space it should be about building the infrastructure in your home system as quickly as possible. You have 150 turns before the raiders start arriving. Plenty of time to build up the infrastructure enough to improve research times and credit output to pay for the 'rush' builds.
This is what I have done in any speed game I have started and it works.
Try playing the Dilgar using this strategy (they start with advanced computers so you can build universities from turn 1). Once you get the hang of the 'infrastructure before exploration' aspect, by the time you have the techs to build your ships you'll also have an economy that will support a largish fleet.
Also, the raiders don't tend to bother you unless you have stationed visible ship units/satellites on your home system. The bigger the military you have in your home system the more dangerous the AI sees you, at least that's the way it seems to go whenever I play.
Thanks for the advice. Stupid me. I had no idea you can build the same building on multiple planets in one system
