For a full discussion please check the thread 'Help me (balancing my science and tax rate)'.In single player I suggest the following:
Before Monarchy, set 60% science, 40% tax. Get to Monarchy ASAP then change the government.
After Monarchy until Invention, set 0% science, 70% tax, 30% luxury. Build marketplace/bank in cities (whenever possible build stock exchange as well). Also build one Super Science city which has library/university/Colossus/Coperius/Newton in addition to marketplace/bank. Rely on goody huts and diplomacy to get science advances.
After Invention, you cannot get advances from goody huts. Now maximize the science rate (70% science, 30% tax for Monarchy; 80% science, 20% tax for republic). Also make all citizens to scientists in cities with pop 5 and more. The Super Science City will kick in now so you'll get an advance every 1-2 turns. That helps you to pass by this period quickly. The first goal is railroad, then after that democracy. You may want to build the Darwin's Voyage after RR to get 2 free techs. Happiness should not be a big problem since scientists are content. After several turns you put the citizens back to work to refill the foodbox for one turn (increase luxury on this turn), then put them back to scientist the next turn (reduce the luxury again). Keep this 1-2 rhythm (worker with high luxury rate/scientist with high science rate) until you get to democracy.
After democracy you set 0% science, 80% tax, 20% luxury. Rely on caravans to get one advance per turn (keep at least one scientist in your super science city). Adam Smith's repeated commodity trading strategy will allow you to identify matching commodities. Two continental trading strategy will maximize your trade potential. Your goal is first corporation (freight) then automobile (superhighways). Be flexible at science rate. If you cannot get one advance per turn due to pathetic trade bonus, you should raise the science rate. But soon you'll be quite comfortable with your trade revenue then you can reduce the science rate according to the situation.
After automobile, you can build superhighways and the trade bonus will be huge. At this point you can set whatever science/tax/luxury rate you want and still get enough money and science from trade. Adam Smith prefer maximizing science, I prefer maximizing tax. Don't forget to build airports when you discover advanced flight.
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