Tech Tree
There are a few techs that are going to be pretty essential early on in the game. Ship research is probably one of the most important, you should almost always research your respective races Long range frigate (Javelis,Illuminator,Assailant) as soon as possible. The long range frigates are excepional at killing the common early game light frigates (Cobalt,Disciple,Skirmisher), and should be the backbone of your fleet early on in the game. That goes for SP and MP in most cases. Other critical techs include the Ice/Volcanic colonization techs(if there are several of said planets nearby) and repair bay tech. The most useful techs you'll need are the ship techs. Each ship fills a vital role in the fleet, and the more variety of ships you have, the stronger your fleet will become. But remember that strong fleets have strong backbones, meaning that the bulk of your fleet should comprise of good damage dealing units like Long range frigates and/or Heavy cruisers.
Economy
The others are right, that you should expand quickly, but only as fast as your economy will allow. To streamline this process, when you capture a planet make sure you have enough resources to put points into planetary infrastructure (1 for asteroids, 2 for all other planets). Your economy suffers when you colonize a planet as an underdeveloped planets will take money from your credit/second income rate. By putting points IMMEDIATELY into infrastructure you'll reduce the amount of time that planet is underdeveloped, minimalize its impact on your economy, turn it into a money maker quickly, and allow you to move on to the next planet without delay. Te easiest way to expand quickly is to use the capital ship with the colonize ability as your first Capital ship, and the colonize ability as its first. This will allow you to enter a neutral well, destroy the siege frigates guarding it, colonize it and then build a few static defenses to help handle the rest of the militia guarding the planet. Build a repair bay first and you can take your cap ship out of danger from destruction by even the most heavily armed militias. Throw in a few turrets to help with the killing part and you can take planets with your cap ship alone, while a second fleet expands in another direction. This is just one strategy (but a popular one), so don't feel limited by it. Once you've set up a decent empire of planets you can then start focusing on the planet upgrades. Also this way you can sort of specialize planets, planets on the inner part of your empire wont need the health upgrades or tactical upgrades (so your not wasting money there), while the outer planets will benefit from more health and tactical. (especially if they border the pirate base or enemy territory)
Culture
Culture is important to the game in the long run. It increases planet allegiance by 10% (somewhat slowly) which in turn increases your planets credit/metal/crystal output by 10%. While that may not seem like much, a single culture beacon can effect several planets. The best place to put them is at planets with lots of phase lanes attached to them. The culture will travel along the phase lanes to adjacent planets, and then will travel (more slowly) along that planets phase lanes to its adjacent planets and so on. The spread becomes slower as the "signal" gets weaker the further from its source it gets, so its a good idea to put a culture beacon ever 3 to 4 jumps to keep the signal strong. The other benefits of of culture are that its a great defensive tool and a marginally effective offensive tool. When your culture signal is strong at a planet, your enemy will not be able to colonize it. So if your empire has a strong web of culture and your enemy gets in, they wont be able to establish a foothold in your territory. That being said, you should note that capital ships repel culture, and so does enemy culture. Having a strong culture web will often overcome the repeling of culture by a single cap ship, but the more they have at a location, the stronger the repulsion, but this goes for your cap ships against their culture as well. Also, the further a planet is from a Homeworld, the lower its allegiance (to a minumum of 25%). Using culture on your border worlds can often drop enemy planets far from their homeworld to a 0% allegiance, which will make it turn neutral, at which point you can simply send in a colony ship/cap to colonize it and take it for your own.
Fleet Size
You should only increase your fleet size when 1) you need more ships and 2) your economy can support it. Keeping a close eye on your opponents forces with scouts will give you a good idea of when you'll need more ships. The first level of fleet supply is easily supported by the economy you start out with so dont hesitate to get that one. But be careful, at higher levels, it will decrease your economy more, making it difficult to rebuild your forces if you take heavy losses, so with a big fleet, don't hesitate to retreat and save your ships if you get overwhelmed. Losing a planet (unless its your homeworld) is much less hurtful to you than losing your fleet.
Pirates
Covered above.
Expansion
Covered above. Although note, tradeports will boost your economy in the short term, while population is more of a long term bonus (as it take quite someitme for your population to max out wonce its upgraded.)
Refineries
I agree with the previous assessments of refineries. They're beneficial in the right situation, but often the logistics slots they take up are better served with other structures like tradeports
Static Defenses
Repair bays are best. Its a good idea to group your planetary structures close together so you can cover them with repair bays and turrets much easier. Against the AI, turrets and hangars are pretty useful, but against humans, better not to bother. Just be sure whatever defenses you build, to supoprt them with repair bays to keep them healthy if they come under attack.
Planet specilization
Mostly its a good idea to spread out your labs to multiple planets on your inner empire, that way if you lose a planet, the effect on your military/economy will be minimal. Other than that, just note that desert planets make wonderful specialized planets. They have the highest number of logistics slots, allowing you to outfit one with a huge trade facility, or a super ship production planet. But like in finance, best not to put all your eggs in one basket.
