This is difficult to answer because experience is really the best way to learn this, although I will give you a few pointers, to help in the first half hour-ish.

Tec.
I advise TEC to new players because they are the simplest race. Get credits so you can buy minerals.

The emphasis here is trade ports, however, you should build a fleet first, then get econ. Max out your units to the second tier of units, and then focus on econ as a TEC. Key is to max out with LRMS.

Also, TEC in general doesn't need to go too far past tier 2 in logistics labs early in the game. You reach logistics lab at tier 2, there's no need to go futher. You can then build 2 military labs and build a fleet.

The part where it's you is do you want to go econ after this initial build-up or go military. It's a matter of Pref.

Vasari.
Middle Difficulty Race. This race emphasizes getting resources to sell for credits.

You only need 1 military lab as Vasari early, as that's all you need for assailants. You should get two logistics labs as Vasari to start as well. You can colonize foreign planets and there's a key tech that Vasari should get early with econ. It's the +% Vasari resource extractor

Advent.
Hardest Class. you rely on planet income to make units that rely on abilities to stay up to par with your opponent. The best advice I have is tech straight to Illuminators.

Double post, my bad.

As TEC, during my early games I found I had a negative economy because I never upgraded my planets. Thats really key. You HAVE to upgrade the population on your planets/roids or you'll go broke. You actually have a negative income on your early colonies until you upgrade them. Do it to your home planet while waiting for your cap ship.

Once you've upgraded the population and tossed in a few tradeports, you'll find you have money to burn ( against the AI at least ).

Fleet builds.. thats a whole other post.

I'm going to emphasize Harada's point. It's essential to upgrade the population of your planets, especially because when you obtain a new one, it's a DRAIN on your income.

I tend to play Advent in 4v4 comp. stomps with three of my friends. I try to make a beeline to LRMs/Illuminators, build a few of those for good measure, then worry about economy. Doing this gives me a pretty good base to take over the asteroids and other planets right near me. A few Illuminators plus a cap. ship (I used to go with the hangar guy, but now I've switched to the colonizer) works well.

I do find myself buying crystal early game to make this work, and I have to rely on the AI not making an early rush.

-HM

Rule of thumb: Don't build military upgrades until you have enough ships to make it worthwhile

Another rule of thumb: When considering economic upgrades thing of how long it will take to get a return on your investment. If the time to return is long and you need it now, then wait

I'm new to this game (though not to strategy gaming) and I am finding that taking over and improving planets is important for your credit income. Using whichever ship has the ability to grab neutral mineral deposits in asteroid belts or the like is a handy way to increase mineral income without having to attack another planet (if you don't have the military to do so).

Some players suggest holding off on the volcanic/ice upgrades, but I've had some random maps where the only 3 planets I had nearby were all volcanic and in those cases it makes sense to tech rush for the volcanic upgrade.

The best starts I've had so far were ones where I was able to nab a string of planets early and upgrade them to get the credits rolling in. Then it's a matter of building a huge fleet and going to bash some hulls.

I'm still learning as I'm quite new to this type of game, but it seems from the amount I've played so far that many of these decisions are dependent on your situation, and that can only be determined through scouting. For example, as futurehermit noted, you may get on a map where the closest worlds to your own are volcanics. It would therefore be foolish not to research volcanic exploitation (or whatever the other techs call it - I've played only TEC so far). Otherwise, you're passing up sources of income. Conversely, if you're surrounded by those asteroids that must be captured, you'll need to build a colonizer to be able to exploit them.

So, many things are situational. Intel is key, and that means building a couple scouts is a major priority so you know what direction to funnel your resources into for a balanced economy.

That's the way I see it, anyway.