As said colonizing planets is important. If you cannot get enough planets in the beginning to push your economy etc so far you are able to develop you have lost. Do not rely on the first two planets and believe you can get far this way.

The first thing you concentrate on is building colony ships. Thus you buy the first factory - if you have manufacturing bonus tiles - perfect. Focus on military production on your homeworld to push colony ship production. A ship every few weeks does fine. Remember there is the production capacity slider, that can boost your production strongly. Dont mind going into minus for a bit of time, faster expansion is better than have 5k treasury all the time. Use your automated scout ship and hope for cash in anomalies. Consider buying a colony ship if you actually have to fear losing a good planet to an enemy you just discovered. That is a thing of experience, you have to estimate how fast they can go and if it is worth the money. The problem with planets is - they cost money at first. Cut this down by not doing the mistake of building every tile on every planet instantly you get in your hands. Planet income is the taxes you get and taxes depend on population. Citizens in GalCiv II are very shy and need time to open up sexually, so you will have to wait till the planets get populated. Remeber every building you build does cost maintenance and this will get you into debt very fast if you do not have the population. You have the planets you have - just leave them growing fopr a while before you start building them. Optimizing what to build when is a thing of experience. Many things you just learn by trial and error to get the feel for the game.
Point distribution at the beginning is also a good way to buffer this a bit, mind pop growth, economy and morale (which is economy in fact because more morale means more taxes possible). Morale btw is another thing. Pop growth is morale dependent. 100% morale means maximum pop growth. Keep that in mind. Super Breeders get decent pop grwoth bonuses if their morale is kept at maximum. To me for other races it is enough to just keep it over 75%.
Colonizing - good planets first is good, but take care you do colonize area-wide. You do not want to get a ragrug in your area, that makes it impossible to get a decent influence because everywhere is the enemy. Do not underestimate the quality of class 1-4 planets. Actually those are better than 7-9s. You know i have had a small class 1 planet i called "poor Peter" because it sucked. Peter became class 14 through Terraforming techs etc while my 7s became 9 or so.
Techs - yes, quite hard to say which ones. Depends on strategy. Look at what they give and what your demand may be at the moment. Weak economy? Go for economy techs. Want to get a diplomatic boost over others and to trade techs? Go for diplomacy. And so on. Do really look what they give and decide what you need at the moment.
Military - especially in harder difficulties it is at first hard to keep up technologically with the enemy. This is what military starbases are for. You can build small fighters and use military starbases for assist. This just pushes your military rating. Military rating is important, because it means power. You are a frightening enemy so the others will be glad to kiss your a**. It is not about being able to attack, its about being competitive on a military basis. Once the enemy realizes you are weak they will begin wanting money from you or smush you right at the beginning as long as they are able to.
That makes technology trading easier as well. btw - do not trade diplomacy techs. Diplomacy and military are the keys to get what you want.