Getting destroyed right after early game

-Consider another race.  Arceans speed disadvantage hurts a lot in a huge galaxy. 

-You should be expanding as relentlessly as you possibly can.  Every planet chips into your research and production efforts.  High PQ planets are best, but you should pick up the sixes and sevens too.   Five or ten planets isn't much on these settings; I haven't played enough games at all sizes and frequencies to be sure what you want but you should be colonizing like a mad bunny.  Trade 'tech and from the minors and majors to finance it all.   

-At Tough at least, you don't need an extreme strategy all-labs / all-facs, you just have to be grimly determined to outbuild and outexpand everyone else.  I spend very little production on military; I trade 'tech or influence for warships when the natives get uppity, I set the AIs on each other as soon as I possibly can, and I concentrate on colonizing and developing my economic base.  

But if I expand even more I'll run out of money very quickly. The colony maintenance costs + building more colony ships really takes a toll. I have no idea how to finance it. And should I build anything on the new colonies at first? Even farms?

Also, tech trading is off for me. I don't really like the mechanic in any civilization type game.

Getting past the first stage is the toughest part.  In my mod, I imagine it's even harder to keep up with the AI since I took out all the fat and wasteful research.

You've identified the limiting factor - the economy.  You need to get comfortable with the idea of running a deficit while you expand, then balancing the budget and pulling ahead.  Don't let your deficit stop you from expanding.  Your tax income is based on your population.  The more planets you grab, the more population growth you have, and your income grows.  So even though your colonies operate at a loss right after you get them, they will grow to produce a surplus.  If you stop at only a handful of colonies, you're cutting off any future growth.  The AI essentially plays that way.  People think it's cheating, but it's simply going all out on expansion without considering the drawbacks.  It worries about the downsides after it owns half the galaxy.

With that in mind, anything you can do to accelerate population growth and boost your economy will help. Key technologies for me are:

1 - Space Militarization (War Rooms for the Arceans).  May seem unrelated, but it allows you to build Recruiting Centers.  +20% pop growth and +10% economy on your new colonies helps a lot.

2 - Xeno Economics.  +10% overall economy and allows you to build Advanced Market Centers.  You may not be able to afford factories and labs on your new colonies, but building one factory and a bunch of Markets/AMCs will help your economy get off the ground.

3 - Xeno Farming.  In the unmodded game, there's no reason to build farms until your planets are at max pop.  In my mod, the basic farm gives +5% to pop growth and morale.  Both will help to ease your economic problems.  In v3.1, there is no morale bonus, but a 10% pop growth bonus.  In either case, it probably doesn't hurt to build farms fairly early on.

4 - Xeno Entertainment.  A big overall morale bonus keeps the people happy, driving population growth and allowing you to raise taxes.

Other than that, if you can manage to snag a morale or economic resource it will help a lot.

Thanks a lot, will try those techs. And do you think I should be producing all the farms I can on the new planets? Or will that cost too much?

Also,with quick expansion I run into the problem of having to get my production from 100% to around 50-65% to avoid being completely bankrupt. Is this wise or is there something else I could do?

Maybe it's just me, but I wouldn't spam farms all over new planets...

I've found that it tends to REALLY kill your morale.  Which will make your population grow slower, and will make your planets easier to conquer.

Even when playing as the Krynn, and having all the morale boosting structures possible (plus I put the best one on a booster tile for morale), I found that my homeworld was getting grumpy constantly once I was over 20b population on it.

EDIT:  I was using Tolmekian's mod (V3.0) in that game, BTW.

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!

It's worth noting that it's harder to get the economy going on the bigger maps because the tourism function works differently. As a test, I started a game on a tiny map with 2 opponents and got 80bc due to tourism on turn 1. On a gigantic map, with the same race and number of opponents, I got just 4bc. You can take some solace in the fact that the low tourism hurts the AI, too.

If you don't mind using slightly exploitative tactics, you can keep your economy afloat by trading influence points for money. Those points are just UP votes, so they're essentially worthless, but the AI will gladly buy around 500ip for 100bc, depending on your relative diplo ability. Heck, with enough diplo bonus (the super diplomat ability would really help here) you can buy planets with nothing but influence points.

In the early game, if you're trying to grow your economy and find yourself getting dangerously low on credits, focus on just one aspect (Military, Social, Research) that is going to help you.  Put as much production behind that as you can, and aim to just stay afloat.  When you've done what you've set out to do in one aspect, switch to another.  The morale hit from going into the red will hurt your population growth just like overtaxation.

It's not so much the quantity of colonies that you have, as their significance in your greater plan.  The way I see it, if you have just the colonies you need, you suffer less economic strife in the beginning and proceed to research your favourite method of acquiring planets.

Addendum to the morale hit from "permanent deficit": You can maintain a negative cashsupply for quite a while, but after a certain amount of turns the game will warn you that it is starting to hurt morale (it will show a sad smiley face in the lower left corner, near the money and morale indicators and will present a pop-up next turn), this is the moment to sell your tech for bc's to get you in the plus (preferably to minors). You only have to be in the plus for one day for the whole counter to start over, negating the popularity penalty.

Sidenote: Selling influence points for credits is a bit too gamey for my style. Why does the Ai even offer anything for that?... It boggles the mind...

Two more things i do to keep my economy from imploding as I colonize like mad:  

Get two levels of miniaturization and one of sensors, build (or better, convert from bought enemy scouts -- I like my opponents blind and stupid) tiny survey vessels, and put 'em on autosurvey.  If you work up to about a dozen you just own the anomalies, and those 250 and 100 bc boosts seem to come just when needed.  

Don't build factories first; start every colony building a recruiting center and even an advanced market center.  Yep, it takes ages; but you're not financing either the factory maintenance or the factory output.  And i don't build farms, even with the mod, before nearing the cap -- though perhaps I should.  

Some more ideas or further expansion on ideas that were already posted above:

- Especially in a huge galaxy, planet grabbing is key so make sure you have 1 planet that can produce colony ships fast + add some engines on those ships. Get a few planets up and running, colonize the other but don't build anything on them yet because the maintenance costs would kill you. Leave those planets empty until either your economy has improved or until the planets become almost self-funding

- Tech trading with the AIs is essential in the race to stay ahead research-wise. Actively trade technologies (no diplomacy technologies as that would weaken your position in future negotiations) and influence points (up to 999 at a time, due to a bug 1000 IP or more are not valued by the AI) for technology or even some cash

- As mentioned by other people before, farms are only interesting if you've reached your maximum population on a planet and even then there's a debate about whether farms + morale buildings are really better than just adding some banks

- Keep the morale on your early planets at 100% (or 76% if 100% would cause too much of a deficit) to get a boost to population growth. Note that this is impacting planets individually, so it's not your overall morale that matters but for each planet separately.

I don't play ToA, but I do still play DA some, and many of the same pronciples apply, IIRC.

You should consider different racial bonuses, I believe.  I did not see any economic or morale bonuses on your list.

Economic bonuses are critical, especially in the early and middle game.  You need to maximize your income so as to put off the moment you might have to face bankruptcy, etc.  Similarly, morale bonuses allow you to increase your tax rate, other things being equal, which also increases cash flow.  This then allows you to keep morale at 100% longer at the game start, which allows more growth of tax-paying population.

BTW, be alert for green anomalies that can be mined.  I have even "upgraded" a colony ship to a constructor to allow me to snag a green mining anomaly.

Consider building nothing on most new colonies for a while.  That is, pick one or two to build a spaceport on, maybe ones with a manufacturing bonus tile, or one that gets a production bonus when you first colonize it (when you choose "evil" or something).  On the others, wait until the population increases at least enough to yield a positive tax cash flow.

In DA, one approach is to run the research path to economic capital, build it on your homeworld.  Next, get sensors and ion engines and build a couple more scouts so that you can harvest more of the anomalies, several of which give cash.  If one blunders across a green anomaly, consider "upgrading" it to a constructor right there and grab it and send more constructors for more economic bonuses.  Soon after that, run the path to political capitol, and build that also on your homeworld for the morale boost (especially on a morale bonus tile).