Please give me some tips on starting off

The order you research technology in depends on your play style (ie, pacifistic, warmonger, merchant, etc) but no matter your strategy, you should initially colonise as many planets as possible before the other civs get them.

Your first few turns will depend on what type of victory you're going for.

If you want to win via conquest, you'll be getting weapon techs and planetary invasion sooner than say, diplomacy ones.

(This doesn't mean you can ignore earlier techs, anything that takes you more than 15 weeks to do is too long so you should research some other techs first)

In terms of colonising planets, you should usually get as many as you can, starting with the good ones. At the start, I'd say anything below level 6 isn't worth it.

(This is on default settings)

Another thing I like to do is cut my tax rate to 0% at the beginning to get higher approval and therefore, higher population growth. I'm starting to realise that this isn't ideal for all games though, but I think it works well if you're going for an influence victory.

Still, I'm hardly an expert, so I guess somebody will come blow my tips out the water with some much better ones.

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.

The two largest factors that shape your entire game is:

-Where your starting planet is in relation to the other players and.

-Your starting planet's bonuses

These two elements can literally make or break your civilization, because if you start too close to another race you will be caught up inevitable battle for resources/planets while the other players in the game expand unchecked and unfettered.

Your home planets starting bonuses are very important because it is (likely) to be the planet you rely own in the very critical beginning stages of the game so if you have a homeplanet that has no bonuses or crappy ones you will be fighting a uphill battle from the start and you can only hope that you will discover a better planet soon to replace the pile of crap you started out with.

If these two things work out well for you your well on your way to becoming ruler of the galaxy! MUAHAHAHAHA.... sorry.

I agree that it can be impossible to win if you are starting somewhere in the corner with to planets, the next one aeons away and already captured when you arrive.

But in my opinion every game you can get enough other planets can be rescued if you play well.