It's probably due to my lack of knowledge more than anything else (still fairly new to the game) but I find the following virtually essential to get my economy working:
(1) Racial Economic Bonus
(2) Racial Population Growth Bonus
(3) Racial Influence Bonus
(4) Anomaly Harvesting
(5) Rapidly Tech up to Republic
(6) Rapidly Tech up the financial structure trees
I find that without doing/having these the early game rapidly becomes a tedious and unpleasant grind. Having/doing these forces you down a particular path, but deals with the economic problems fairly effectively.
So far I reckon that economy is pretty much about population growth, lots of it, and fast - supported by appropriate racial abilities/techs. Which is fair enough; but at this stage seems to somewhat limit the approaches to playing the early game.
One thing I have just started experimenting with (which seems to work quite well, although it's too early to tell) is to have dedicated colony/transport ships to transfer population from my homeworld (and later other high population worlds) to newer colonies. This definitely speeds up the development of an economy.
Personally I would love the game to include some form of "pillaging" option for when I play a more militaristic race. Something along the lines of:
(a) Ship module to allow salvaging (and hence selling) remains of defeated fleets
(

Ability to scrap (and hence sell) structures from conquered planets
etc.
There are quite a few threads out there on the economy worth tracking down, or hopefully someone with more experience than me will chip in.
Franbo