First of all, you should know that I am still playing DL, so my advice might not necessarily apply to DA, and that I usually play on Tough or Painful difficulty.
I usually set my sliders to about 20%/40%/40% (m/s/r), with some slight changes as need arises. My main economic strategy is to periodically sell some low end techs to other civs to supplement my treasury, so that I can run a deficit in income (which almost always happens when you run at full capacity). Also, don't let your approval drop to low, higher approval means faster population growth which means increasing economic capacity. Personally I think that 60% approval is the absolute minimum to satisfactorily increase my population, but thats more of a hunch than anything, I haven't done any tests. In any case, the higher the approval the better.
For research I devote my secondary planet (the one in the same system as your home world) to research buildings (its too small to be satisfactory for anything else), and I only build research on other planets if there are bonus tiles. This has proven to be adequate to keep me technologically competent. Speaking of technology, try to research economics and morale techs to help alleviate your economic strain.
Personally, I don't bother to keep up with other civs' militaries early on, because it is totally irrelevant without planetary invasion (unless you have starbases that can be destroyed). With good diplomacy I can usually avoid war by paying small tributes or otherwise gaining favor (which is much cheaper than building a military in the short-term; it can backfire though in the long run if you're attacked anyways).
But other than that, just try to grab as many colonies as fast as you can, skip over the small ones in favor of landing large, high PQ planets (I would skip anything lower than PQ 8). You can always go back for them later, and if the AI gets them they will soon flip with your influence.