I would say the answer to your question is going to vary with circumstance from game to game. Here are some guidelines and scenarios.
Once my research rate has dipped to 40%, it's time to develop more infrastructure to bolster the economy. This is given running a CE, hybrid, or farm based economy. If I'm running specialists, my research rate is usually zero and I'll expand until I'm close to running red. Then it's time to sack cities for cash.
Gold, silver, or gems will have a huge impact on early finances. It ranks right up there with copper and horses in the early game. If you can land one of these happy and money resources, it makes the game a whole lot easier.
If I'm playing a creative civ, I'm usually content with two cities until I'm ready for a war. The reason being I can build military, wait for the AI to drop a city, and then take it. Most AIs don't seem to place culture a high priority so a lot of the of time you can capture a city and won't have too many cultural border issues (early in the game).
Whipping via slavery will help keep early maintenance costs low. It's relatively easy to grow back those early population points so whip them away.
War - taking out neighboring cities (barb or AIs) will generate nice income to keep you in the green for a while.
Trade - Once currency is in, you can trade techs for cash. Trading backwards techs for even a little coin is usually worth it.
Scouting - Good early scouting can generate a lot of income from huts. This is of course random and luck based, but can be very effective
This is scratching the surface. There are many ways to either reduce maintenance or increase your treasury, both of which have the same effect, maintaining a high research rate.