I usually play on the larger size galaxies with abundant anomalies. I've been using cargo hulled survey ships for a long time. I usually build 3 or 4 as soon as I can and just let them go. When a ship closes in on a star system I am interested in, I will take it out of auto survey mode to see what habitable planets are in that system and, when done, put it back into auto survey.

I am not hurting for colony ships since I can usually find enough money to build them in a single turn.

The bonuses from the anomalies really add up quickly when playing the larger galaxies. Also, the research-speed-up anomalies you come across will give you a good tech boost early on in the game when you are researching the core techs.

After the anomalies are gone, I will put the ships into auto explore mode. I like to upgrade my survey ships into freighters. They will usually be on the other side of the galaxy which maximizes my trade income and, in addition, I don't have to waste time sending a freighter across the map. The freighter's home planet will be the one on which the survey ship was built, normally my home planet.

Either that or have anomalies appear randomly throughout the game, instead of having them placed only in the beginning.

I know I am new to this game, but I have been reading the forum posts and experimenting with different ideas. For speed, I build a cargohull with engines only - easiest to build a hull then upgrade to engines, and I go straight for the stars looking for planets I can colonize (a colony module is size 20 so I don't use it initially). When I find a suitable world I upgrade to my cargohull with colony module only design. I get 1 colonist, just enough to claim the world so the AI can't. This worked pretty good on a small map playing the Yor against the Drengins on tough. I had rare everthing - only 12 colonizable planets total, 2 home worlds. and 10 others. I got 10, Yor got 2. By turn 30 Yor was so far behind I started a new game - didn't bother to finish. Thing was, as long as I could build a cargohull in 1 turn, I was gold. My capital was 3 factories and a research building until the rush ended and my research was focused on tech buildings. Yeh, on a larger map better engines would have made a difference, but a small map is only 9 sectors, why bother? After the rush, I had 9 worlds with 1 colonist each, so my priority was growing people and ferrying them to the worlds. By turn 30 all 10 worlds had 6B except my home world - it had 12b. Every planet had at least 1 factory, a research building, an economy building, and 6 or above also had a starport. I've played games where PQ3 worlds were able to support an industrial center and spaceport, produce 30 mps a week, AND make a profit under a star federation government at 35% tax rate, but initially I just que up 2 eco builds and leav'em.