struggling a bit

Fleet first. Research second. If you're not number one in the fleet ranking you're doing it wrong.

thanks for the advice

lets get back to it

bert

Play the TEC to begin with- they have a good balance of ship costs to technology. Advent ships are cheaper but less powerful, and the Vasari are expensive.

Ensure you have a good supply of crystal. Build a colonization cap ship first and use it to grab an asteroid or two (depending on the map) to get those resources in.

Modifying Cataclysm's advice, research weaponry first. No point going into a fight without at least an upgrade to your primary weapon system. Besides, you need at least 2 civilian stations before most of those upgrades are useful, and for that you need a new planet...

Make sure that the teams are LOCKED in the game settings, otherwise they'll all form alliances with one another and gang up on you instead of fighting each other.

I completely disagree with Johnathansmile's advice.  If you look at what races the good, experienced people play online, they play Advent or Vasari and with good reason.  I suggest learning to play both and avoiding the TEC.  (When you come online to play it in online multiplayer you'll thank me for this later.)

The Advent have the most powerful long-range-missile (LRM) frigate in the game in the Illuminator and they have the best fleet-enhancing capital ships (Progenitor Mothership--shield restore, and the Halcyon Carrier--faster wapons firing rate and anti-strikecraft).

The Vasari have an excellent capital ship in the Evacuator Mothership (nanite attack against other capital ships, level 6 suck planet) and they also have the potential to use Returning Armada (think unlimitted free ships).  Note that RA is getting severely nerfed for the 1.1 patch.

Those two races have some other great ships, too.  The TEC tends to get squashed by both of them.  Also, contrary to popular belief, the TEC do not have the best economy.  IMHO, Vasari has the best economy for a number of reasons, believe it or not.

Highly depends on how long the game lasts. The Vasari get a great boon that blowing stuff up gives them some resources, and the whale's planet drain is great for ore/crystal. But given a long enough game (such as the ones on big single player maps), the TEC being able to cram 2 extra trade ports on every planet goes a long way, not to mention the research that  gives them money whenever all other empires spend money.

The TEC has Vasari outclassed in that regard Their economy is easiest to start (cheap ships, trade ports with 2 labs), and evolves into a free credit factory if the game goes on long enough.

Regardless, it's bad advice to tell someone to ignore playing a race. Let them try for themselves to find which they like best.

As to some advice:

Like Cataclysm said, don't spend too much on research early on, especially ship weapons. It takes a while for the bonus from the research to outweigh the bonus of just building an extra ship (beyond the basic damage output, another ship also adds shields + hull to your fleet). It is a very good idea for all races to get the long range frigate hull unlocked (Javelis LRM, Assailant, or Illuminator). Those ships do wonders that your light frigates early on are very jealous of.

The second part is getting your economy going. Don't over-extend, and always make sure you upgrade the new colonies' infrastructure so they start making money instead of sucking it away. As a rule of thumb, I never colonize unless I can afford to upgrade them right away. Just one will do it for an asteroid, but actual planets will need 2 to climb out of the red, though. This varies a bit by planet type, so be sure to check their info cards for the penalty change in the upgrade. Then set up those trade ports. The TEC gets them very early with just 2 civvie labs needed (which you'd have to build anyway to unlock volcanic/ice colonization, win-win) so they can start churning out extra credits pretty quickly. I usually find myself with an abundance of metal early on and a lack of crystal - so while you're waiting for your crystal to trickle in, list that metal on the black market (not the quick-sell!). The AI will buy it especially in the early game, and you can get some great money out of it.

Third, never upgrade fleet capacity until you need to. Every upgrade increases resource upkeep which is irreversible, so once you upgrade you're stuck eating the upkeep. This basically means you need to balance expansion (and by extention, the economy since expanding gives you more taxable planets, mines, trade ports) and fleet production. This is really the hardest to get a feel for but remember - it's the ships that do all the fighting. Get them built as quickly as you can