The majority of your points come from numbers of producing buildings and percentage of resources, so large worlds with favourable atmospheres and high values in a needed resource are a good start, and you will want your research to pick up too, which is not affected by the quality of the planet, so large planets again. The maximum facilities of a planet is its size x 5, so tiny planets can only have 5 and huge planets can have 25. Unfavourable atmosphere divides this by 5, so a huge planet with a bad atmosphere is as good as a tiny one with its races atmosphere. If you capture some of an alien race with a different atmosphere then you can use them on appropriate planets, so long as everyone on a planet breathes the atmosphere it will be regarded as favourable, but just a single million inhabitants with breathing difficulties will ruin it for everyone... There is also a technological solution via planetary engineering, but that is expensive and time-consuming, although it does reinforce the point that atmosphere is more important early on, but later on size will be the thing you can't fix. Also bear in mind that shipping in aliens to work inhospitable planets could be viewed as slavery, and converting millions of your population into raw materials to quickly get rid of the non-breathers could also have role-playing consequences...
Expansion is good, warp points are comparatively easy to defend, so if you can get to one first and sit on it then it will be easier to hold that territory for later. As stated above, planet space is the biggest factor in production, more territory=more planets=more space... Also, some planets have ruins on them, these are basically free or unusual technologies, getting dibs on these is good, as instant or unique technology improvements are otherwise difficult to come by...
So, yes, expansion is key, try to get something to hold warp points, mines and satellites work well early on and just getting a couple of warships there is probably the quickest. Be advised that some people build nasty colonisers that ram you, colonisers are significantly bigger than frigates and can win with this tactic, so consider telling your ships to keep their distance via the, ummm, you will probably want to look through the empire options at some point, it is just a little bit of a mess in places, feel free to ask questions but I don't much care to try to explain the whole thing from scratch.
Short version:
Expand quickly, both territorially and economically, Secure the borders of your territory at the warp points. Also, make sure that you have 1 space port per system(map) or the merchant trait or else yours colonies in that system won't produce any resources... System means Star system, sector means a single hex, and is typically used to describe a single planet. Sector and system are easily confused, at least by me...
