I think this is incorrect; low approval means lower POPULATION growth, and the higher your population, the MORE money you make. Increasing taxes will lower aprroval and therefore SLOW population growth, and if it is low enough, cause you to LOSE population, but that's really low, like under 30% or something. So basically, if you have low taxes, you wont get much money at first, but your income will increase fairly quickly with time, because you have more people to tax. Putting high taxes means you have a larger income, but that won't expand very fast, so as you get bigger ships and improvements you may not be able to maintain those budgets in the long run. Of course, you could set the taxes really high and then build several entertainment centers to offset the low approval; then you will have a high budget that increases very fast.

You are correct however, about them hating you when you have less money. You recieve a morale penalty when you are in debt (I think it starts when you are <-500 bc), and this penalty increases over time the longer you are in debt.

Mainly its all about balance.

This is how I usually play. Early in the game I keep my approval around 50% and I dont go lower than -500 bc to avoid the morale penalty. I do this by lowering/raisng taxes and, yes, lowering production capacity when needed. I will usually build one entertainment center on each world to help out too, then more later as population grows. Building economic centers helps too, but their effects are negligible on early colonies, wait to build them when you have a decent population. I will also ignore military production(fighters, trade ships, scouts, etc.), putting 50% each into social and research, and then contracting colony ships as needed (though this might actually be more expensive, any more experienced players know?). This is a little risky and can go pretty badly if I turn out to be neighbors with the Drengins or something, but I play a custom race with a high diplomacy racial bonus, and I am usually able to sweet-talk my way out of a war. Also, with my diplomacy I can usually get a lot of cash by trading techs, remember you can trade the same tech with every civ, so every 50 turns or so I clean out everyone else's treasury by selling them all the same basic techs. Using this strategy I can survive off a negative income for a while, so I can keep my people happy with low taxes while still having a high production rate. Eventually, with the right amount of farms, entertainment centers, and economic centers I can be totally self sufficient, and maitain a green approval rating (70%-100%). I will still usually operate on 50% social and 50% research throughout the game, and just contract military ships as needed.

True, in DA it is more difficult to manage $$$ than in DL. At the beginning of the game I’m always playin' to the limit of my finances, keeping the moral above 50% it's enough and always look forward trading too + building 2-3 economic starbases. Often you have to slow down everything (50-70%) but later on, if you manage well your planets the income starts quickly growing which is mainly welcome to bear your army (ships are expensive, therefore quickly replace the obsolete ones...).

I confess this is one of the more difficult part of the game, sometimes I even had to give up in the middle of a game, cauze went bankrupt...  

DA 1.6 final

Early game I keep my taxes low enough to have 100% growth. Get that pop up there fast. More Pop = more $$$.

I keep my production slider at 100% and deficit spend until I get close to -$500. Then I'll cut my production to 0% for enough turns to get out of the red, then set it back to 100%...rinse and repeat.

I'll research economic techs early...try to get to Intersteller Republic, and get at least the second level of Trade Centers.

I'll trade techs as often as posible to make cash ... and build a second Survey ship on a cheap hull to help farm anomolies for $$$.

I will concentrate on Research early...try to get lots of techs to sell. The aI will not concentrate on econ, diplo or sensors techs early...these can be traded for cash.

I don't build unneeded buildings, building just to fill squares is wasteful; ... and I don't keep a large military until needed. I do not build any starbases (Resource starbases the exception) early on. Not until late year two at the earliest.

I do not build farms on all worlds later on - and will never let a world get over 12 Billion pop unless it has lots of bonus tiles to make it worthwhile. Once pop is at the max, I'll set taxes high enough until I am at 21% morale on the worst world - only lowering them the turn of elections. Don't need pop growth once the worlds are all full.