(Everything below is my text, but based on other ideas long past presented and practiced by others on the strategy forum).
One of the key issues that hasn't been mentioned is that building markets on low population planets doesn't actually work that well because the markets increase income as a percentage of population. So +10% of virtually nothing is still virtually nothing. What does work well is to not build anything on low population planets so the planets expenses don't overshadow its income by very much. Later when populations is larger you can build stuff to increase income or whatever. About the only thing worth building on a new planet if you want to minimize its impact on your income is +population growth projects with no maintenance cost.
Don't rush into Galactic Warfare quite so fast. It is better to raise your social, economic, and military production bonuses early on, and increase your money supply with better economic buildings. It is also better to get some faster movement technologies so your colony ships can win the race to other planets. Instead of trying to build a military early just keep on eye the diplomacy standings, and use your economic treaty and research treaty to keep the two races that dislike you the most early in the game from turning against you. This will give you some extra time before you have to build your military.
In the meantime set your sliders to 1% military, 99% social, 0% research. Then put EVERY planet you colonize on Focused Research. The way this works is the 99% social ensures that all your planets will build new buildings very quickly. Then any planets that are set to build ships will start building them very rapidly as the 99% social roles over to 100% military once all building projects are completed. Meanwhile any planets that complete all social building but which do not have any ship building scheduled will have no building expenses and so if their taxes are sufficient such planets will generate plenty of profits, especially if they have markets. Since all planets are focused to research they will also generate a fair amount of research, especially your ship building planets, which will have a lot of industry switched over to research.
With this method when you research a new building you will have big drops in cash as all planets start building it, but once the building is done you will build up big reserves until your next galaxy-wide update is discovered. Also if you do absolutely need to research something fast you can turn research up and social down, and with the focus already set to research on all planets you will have your research done in no time. Another advantage is that if you are low on cash you can just tell planets that have no social work to do to also stop building ships, giving you an immediate decrease in expenses.
There is one other interesting thing about this method... It does not require, or work well with, research planets. Focused market planets and focused industry planets are all you want, or need, with this plan. Sure if you have a 300% or 700% research bonus tile use it, but otherwise make all small planets market planets, all large planets industry planets, and split the ones in the middle based on need, though most will want to be industry. Under this method all industrial buildings are effectively research buildings as well, so +research is not needed. This saves you the trouble of researching research.
It can take a while to get used to playing this way, but it is actually easier to balance than the three-focused method, which suffers a lot more from one mis-balancing choice (having slightly too many research and/or economy planets is tough to deal with in a sudden war, while this method only suffers if you have way too many economic planets, and sometimes not even then if you want to rush-build everything). There are also many other methods that work, including things like the single-focus method in research for tiny maps with 9 players. So the best advice is to give all the methods a try on a medium map, see what works for you, and then try to expand or contract the concept for other map sizes to want to play with.