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