I totally agree with you about the lack of a good tutorial. I actually plan to get my act together and record a video walkthrough this weekend and posting it on Youtube.
Last time I played (yesterday) I was able to get decent economy, or at least that's what I thought. I had a lot of money in the end and my production was limited by resources which I was lacking a bit (I think buying them isn't a good idea, dunno if I'm wrong): yesterday it was metal, in previous attempts it happened to be crystal.
Basically, your only option with regards to metal and crystal is to acquire new planets. In some circumstances refineries can be used to effectively boost production, but most of the time you'll be short on at least one type and you'll have to pick up the slack on the black market.
You do not want to use the black market too heavily. The rates are absurdly high. It should only be used to correct long-term resource imbalances. If your crystal income is chronically low, don't hesitate to buy some. However, if it's just a short-term thing (you bought a few high-crystal cost upgrades, for instance), let your income even it out a bit.
One common mistake beginners often make is forgetting to buy population upgrades for their planets. Newly colonized worlds will incur substantial costs to your empire, so upgrade them immediately to avoid paying these. Other than that, you should have no problem beating an easy or normal (even hard, once you get going) AI just with the income provided by tax income and extractors.
I think I'm mostly lacking in warfare, as I usually lose too many ships in every battle against the pirates (even for the conquest of a new planet) and they attack me always
This is probably your problem. If you're losing lots of units to militia, that's going to incur massive costs, and pirates aren't going to make it any easier. Expert players rarely lose any units to militia. As for pirates... expert players can handle them, for beginners losing the first bid can cost you the entire game. I do not recommend turning on the feature unless you're experienced, and most experienced players decide they don't like the feature anyways...
Generally speaking, you should not use light frigates to clear worlds. The light frigate is great "search and destroy" unit for chasing down fleeing enemies or support cruisers. It is utterly ineffectively in a straight fight against real unit types with real guns. The Javelis LRM and Kodiak Heavy Cruiser that you will frequently find mixed into militia will utterly decimate light frigates.
As TEC, I strongly recommend two military labs near the start of the game. Research the repair platform and the Javelis LRM. The repair platform is critical for keeping your capital ship alive and maintaining momentum. The Javelis LRM is your "big guns" unit as TEC. It's slower than the Cobalt Light Frigate, but fast enough to pursue most unit types and it hits much harder. It's not a catch-all, but it's definitely the best unit to build the backbone of your fleet out of.
