I just fired up a quick game to refresh my memory. Here is a good way to get the economy going. Choose the Populists, +20 diplo, and +20 morale, for abilities add +30 morale, and +60 diplo. Now your people will be happy and will stand higher taxes, and other will be much more ready to trade and less willing to fight you. Start on simple, small system, tight cluster, and rare for planets. Not many good worlds here, which is fine. You don't want to be bothered with lots of colony ships, and fighting, you want to get the economy going.
Do not build a second colony ship, you may not even be able to use the first one. But if you find a level 15 or better planet, colonize it. Set govt tax income to 90-92%, spend rate to 88%. Your approval will be over 80-85%, and your net income -2 to -3 per turn. Set mil spending to zero, research to 60, and social to 40. No need to change any of these for a while. Build in the following order. In some case you may not have the tech to do so, but can come back quickly. Soil-Habitat-Entertainment-Bank-Research-Fusion plant-Manufacturing-Econ Ex. Towards the end of this chain, Diplo xlators, Manu. Capital, Economic Capital, and Galactic Stock Ex will be available, too.
For research do: Comm-Universal Translator- Medical-Basic Environ-and Diplomacy. Diplo allows you to change to Republic, so do that. Research trade. When that is done, make the military slider 60%, Social and research 20 each. Build two freighters, they will be out in no time. When they are complete, set military back to zero and set social 40, research 60. Send the freighters out to two wealthy planets.
Now set research to propulsion-cold fusion-industrial theory-interstellar refining-zero gravity-nano electronics-sensors-advanced trade and after advanced trade-cultural trade. After cultural trade, you can build two more freighters as before. When they are finished, send them on their way, set the social at 60 and research at 40. You need to get some tings like Economic capital and diplo translators built, and they are more expensive.
After the second set of freighters are on their way, it is a good time to look at your tax and spending. You may be able to raise spending as high as 100% and taxes up around 44-48%. Look in at this every 5-7 turns. Your economy will really start to cook at the trade from other planets comes in. Your economy will be more efficient, too, with the things that you are building.
Most of the important research for the early stages is now complete, use less research and pick up the cheap stuff like weapons theory-battle armor-stellar cart-photons-deflectors-nano freq elec-and artificial grav.
By the end of this, you will have a good position from which to choose how to progress. You can start to slant research more to the military if you like, but you are very well positioned to get way ahead of all ot the others in research and productivity. Build a few constructors. Blue resources to expand your influence cannot be under-rated. Yellow resources will keep your people happy. You can now trade research if you like, because you will have a huge diplomatic edge over everyone. You can buy resource bases from other players for very little, due to your skills. You can increase research for trade, which will, in turn, boost your economy in every phase. From here, you decide how to proceed.
Hopefully this will get you far enough into the game, with a stable economy, so that you will be able to enjoy the richness and diversity of Gal Civ I.