Two answers for you. The short one is just trying to answer your question directly, the second explaining what I do/when I do it with the Yor. I usually play TA on painful with immense galaxies.
Short answer: I usually try to get good relations with a couple of the weaker evil races (who are cowed by my military). Mostly I'm going for a big military and I expect to be at war with most of the galaxy, since I start wiping out minors and whoever is close to me. I focus pretty heavily on weapons tech and bigger ships once I have my economy up.
Longer answer: When I play the Yor, I focus on high production and research. Right away, I research a few techs to boost my pop growth, then I research to their 3rd tier econ tech, where they get efficiency centers. Next I go up the diplo branch to Trade so I can build an econ capital on my homeworld and an efficiency center on every planet I own. That takes care of econ for a good while, esp if I've picked up some money from my flagship. After that I focus on weapons/planetary invasion stuff and bigger ships with occaisional engine techs/sensors/morale/factories thrown in. The key is to strike early and as hard as possible once the colony rush is over.