Most important thing to know is what map size...
If you want help on medium maps I can try and give advice but I know that each map size plays very differently and therefore the priorities change. The guys scoring 200K a shot are all on gigantic. I'm more 20-30K on medium.
Any of this may be wrong. However this is what I believe is true.
From what I can gather the scoring is really crude...
It is based on
1. population (look at getting pop growth as a starter - also the more planets the better)
2. economy (fairly obvious - but it is money earned not money in the bank so spend,spend spend...)
3. military score... if you look at the charts you can see this is based largely on hps and weapon scores. Battles, ship kills etc are worth nothing. Soldiering is worth nothing.
4. tech spend (you can keep spending after the tech tree has finished. Get to research the research buildings early and build lots of them... fairly obvious.
Note that everything that affects these things in game also affects the score.
So those mining resources are essential... also spin control on your main ship producer is nice...
Evil is possibly the easiest to get a big score... cos while neutral has some good stuff in tech and PQ, evil has the economy building and the potential for military spend.
The other big wierdness is that it looks to be a total per turn in each area divided by the whole number of years rounded down... This means you must try to finish the game in a december, if you miss then you are better to eek it out til the following year.
To win as early as you want then I'd suggest going immediately towards planetary invasion and targeting the capitals of the other civs... on suicidal they will have almost completed the plant by the time you get there... (it is often worth putting something in soldiering just so you can take out any enemy planet with a single 500m ship).
Anyway... this may help. It is the way I play and whilst occassionally you just get swamped on Suicidal it is a more interesting way to play.