For most worlds it isn't interesting to try and raise your population above 16-20billion as the morale hit they take around that number is too severe to overcome with a reasonable effort. However, with the popgrowth bonus of tolmekians mod, the farms can reaslly speed up population growth up till that point.
As for the balancing the budget: the Biggest and Most Evil Trick that Galactic Civilization plays, is that it makes you believe that keeping a balanced budget is the smart thing to do. Spoiler: it is not.
NEVER cut back on that production slider, always keep it rigged to 100%! Especially in TotA, maintenance in the early game is the real economy killer, not production. Slashing that production slider really hurts your output, but has no effect on maintenance (so basically, if you cut it by 50%, your production falls by 50%, but your total expenses only by about 25%). Instead, you will have to do something very counterintuitive: lower your taxes! Yes, this sounds like something a crazy Republican would say, but in Galactic Civilization this actually works:
The thing is, your population is your tax base and your population happens to hate taxes. With high taxes they don't want to breed as much (or apply for citizenship or whatever), but if you want more tax income, you need more people. The general trick is to keep morale at 100% for as long as you can possibly manage, then, once it becomes impossible to achieve this for your homeworld, keep it at 100% for your newly colonized planets. Planets with 100% morale grow their population much faster (I forgot the numbers, but it's 2 or 4 times as fast as with morale at 99%), and since this is exponential growth, a planet at 100% will be at 8 billion much much faster than one at 99%. On the other hand, a planet between 41% and 61% will hardly grow at all. Once your planets hit a decent population, you can start raising your taxes till you can actually pay for your expenses. This is why morale resources during the early game are perhaps the best resource you can come across.
As for bankrupty: it is going to happen and it really isn't that much of a big deal. Deficit spending is the way to go during the early game. Use your survey ship to get lucky (+1000bc yay!) to occasionally get above the 0bc mark so the continuous deficit doesn't bring down morale, and/or trade tech to minors (and majors) for money. You'll find that it isn't impossible to keep up with the AI colonizing frenzy (through the Arcean speedpenalty doesn't help you much). Good luck!
