I'm inclined to agree with PotatoOverdose. Colonization, conquest, and vassal integration do really give opportunity costs to one another; you can and should be doing all three simultaneously where you have the opportunity. After conquest, you have a choice about what to do with existing POPs. Under the status quo, they'll be less effective than your own POPs, partially because as a good player your POPs' traits will be minmaxed to the optimum level, and partially because they suffer happiness bonuses. You have three ways of doing something about this: you can enslave them, you can assimilate them, or you can purge them. Enslaving is... soso. You get +20% to Minerals and Food, but this is the same as Joyful's bonus through Happiness which is achievable for essentially all POPs by late mid-game. Slavery only has an advantage for late early-game and mid-game proper. You can use Despotic Empire... but that means giving up choice over leadership traits, which is a huge misfire given how powerful they are. You can use Iron First Governor... but that ties you in to a specific governor and can make you dependent on luck of the draw. You also have to quite heavily gear your ethos towards slavery to prevent the happiness implications from being too negative, which can be frustrating. Purging is just straight up bad, you're severely curtailing your growth compared to assimilation because you're eliminating POPs to make way for good ones, which is a much longer process than just turning bad POPs into good ones directly.
In Stellaris, you win by having 40% of the planets or no other independent empires. There are three ways of acquiring new planets: colonization, integration, and conquest. It is strongly unlikely you can achieve 40% of the planets without using conquest, so being able to conquer efficiently as possible and being able to colonize as efficiently as possible are the best ways to win Stellaris. Thankfully, these two things are orthogonal - you don't really incur any opportunity costs, doing both at the same time is both possible and the best way of playing. Stellaris' combat is quite simple. There's very little strategic depth - land warfare is pointless, you can win effectively any war without it even in MP and the rare occasions you do need it, it can be generated very quickly. Defensive warfare is pointless - all the different fortifications last at best a few seconds against a large fleet. Ship design doesn't matter much - it can make minor changes here and there, but generally speaking, the bigger fleet wins. So efficient conquest means maximizing fleet size.
Fleet size is constrained by three things: naval capacity, mineral output, and energy output. Naval capacity is increased by spaceports, and population. The +5 bonus for building a spaceport is larger than any of the increments, and building a spaceport is cheaper than upgrading them, so it's more efficient to build more spaceports (wide) than it is to improve spaceports (tall). So the best way to increase naval capacity is conquest itself, or colonization. So this merges into colonization, which I'll touch on later. For population, we have four ways of increasing population: growth, robots, conquest, integration. We've reached conquest itself again, so we can ignore that. Growth is best maximized through colonization, because pop growth has diminishing returns - each extra POP for a planet is a little harder to grow than the last. So that goes back to colonization. Robots require minerals and energy, as mentioned above. There's very little you can do to impact integration.
It is also impacted by technology, government, ruler traits, and edicts. Because technology is random, a minmaxing player won't rely on it too much - they will value technology as a category but not rely on any specific technology because of the unreliability; technology is best viewed as a random buffs which you can increase the MTTH for than something you can treat to strategically. The governments that aid naval capacity stop you being able to select the best ruler traits, so they are zero-sum, and ruler traits offer flexibility in other areas, so we can ignore that. The edicts are unlocked by tech again or anomaly, so we can discard those. So we haven't learnt anything from these.
The other limits on conquest we mentioned are mineral output and energy output. So we're looking to maximize these. There are a number of ways of doing so. The first is to increase the number of POPs we have, given planet tiles in conjunction with a POP can produce the above. The second way is to build mining stations, but these are orthogonal again and both can and should be done. The third is to improve the efficiency of our POPs. We can do the latter through a number of ways. One is Slavery, one is Robots, one is Happiness, one is Ethos, one is Traits, one is Techs. As mentioned, techs are sufficiently random they should be perceived passively. Slavery, as mentioned above, is subpar compared to Happiness. Sufficient Happiness strictly dominates Robots as a strategic option (aside from Robots being slightly faster to establish, depending on how well you colonize), as Droids provide +15% to minerals whereas Joyful is +20% (this isn't to say don't use Robots; but Happiness is more strategically valuable). None of the Ethoi directly affect minerals, so we're left with Individualist for Energy Credits as a potential option. As far as Traits go, we have Industrious and Thrifty. In the early game, most of your mineral income will be from Mining Stations; Industrious only affects POP output and so doesn't offer good returns until later. Given Stellaris has a heavy snowball effect as the two things necessary for victory are mutually reinforcing, early boni are always better than later ones. We'll remember Individualist and Thrifty for discussion later. We also indirectly have traits like Charismatic that affect Happiness and so output and so fleet size and so the victory conditions.
So we're typically drawn to the conclusion that what matters is Happiness and Colonization, and the earlier they're available, the better. Our starting planet has 70% happiness (60% base plus 10%); if we can get it to 90%, we're starting with the same boost as Industrious, Thrifty, and Intelligent combined with a little bit more on top! From the start, you can access Moral Democray for +10% if you went Pacifist. Spiritualist gives you +5%. Finding a Void Cloud gives you 5% given Spiritualist. That's our 90%, from very early on. We could go Fanatic Spiritualist to access it immediately, but going Fanatic is usually not a good idea because it rules out width of options. With a Champion of the People for +10%, you can access 90% Happiness off the bat anyway, and also reach it on any same-habitat planet (which will be all your early-game planets). This gives us strong reason to want Spiritualist and Pacifist.
However, we want Spiritualist (eventually) to be on all our POPs, for that +5% happiness boost and also to prevent negative happiness from opposite ethos. Different ethoi is the main obstacle to happiness for conquered POPs, so we want to assimilate them as quickly as possible. We could do this via government with the Transcendental line, but this will do very little in the early-game compared to Moral Democracy, so we have reason to ignore it. As for buildings, there is the Grand Mausoleum, but that's locked away from Democracies, so no go. Militarist's building gives a small per-planet boost, which is immensely soso. Collectivist gives us the Ministry of Benevolence, for an Empire-Wide (!!) -15%. That's a stunning boost, you'll have xenos converging in no-time, all your POPs will be Joyful, and you have +20% output in everything, which is very difficult to beat for any other combination... unfortunately it doesn't go with Democracy.
So, we can pretty strongly say Moral Democracy is the best government, and Pacifist is required. Pacifist does give -10% happiness in war, but that's cancelled out by Moral Democracy anyway. We also want Spiritualist for the Happiness boost. The remaining debate is Collectivist vs. Individualist, and we also need to sort out Traits.
The slavery tolerance from Collectivist/Individualist is pointless because we're not going to be slaving. Individualist's reduced energy credits gives us a slight advantage very early on. Collectivist, however, has a vastly better end-game building, largely better techs, and can access The Collective Self for improved leaders. If it weren't for Moral Democracy, I'd side with Collectivist, but as is...
As far as Traits are concerned: Adaptive is pointless, with the above you'll assimilate POPs so fast you can just use conquered races as easily as your own so you're not going to be worrying much about habitability. Agrarian is too expansive for such a small effect. Charismatic is too small an impact; by the time you have a diverse enough empire for it to be truly useful, you won't be having problems anyway. Communal is unnecessary given the above. Extremely Adaptive same as Adaptive. Industrious doesn't have very much impact in the early-game, where we want it to. Ditto for all the research traits. Nomadic is... mostly pointless. Resilient is meh, we're not going to be on the defensive and even if we were, defense is terrible in Stellaris compared to having a bigger fleet. Strong is pointless because armies are useless, ditto Very Strong.
That leaves us with: Conformist, Enduring, Quick Learners, Rapid Breeders, Talented, Thrifty and Venerable under consideration. Planets outside 30% range or 20% with a sector will still get some small divergence without Conformist, so in the late early-game it can be useful. Enduring means that, given we went Collectivist, we can accomodate for not being able to go with Leader Enhancements. Ditto for Quick Learners, enduring, Venerable, and Talented. Thrifty and Rapid Breeders aid our early output. This is a little less clear, I think. Personally, I don't bother with Conformist; by the time I'm expanding enough for it to genuinely matter, there's other means of coping. It can give a little security but often becomes redundant. Between Thrifty and Rapid Breeders, I'd rather have Thrifty because Thrifty means faster colonization which means faster POPs than Rapid Breeders. Between Quick Learners and Talented, I'd rather go with Quick Learners. Talented costs +2 which is really slightly too expensive given how fast Quick Learners go from Skill 1 -> Skill 2, and Quick Learners are strictly better after that for obvious reasons. Venerable is much too expensive at +4 and you don't see returns for a long time (logically until when your leaders would otherwise have died).
So we get down to Quick Learners, Enduring, Thrifty. The +2 cost of Thrifty is for me enough to push it out of contention; Quick Learners and Enduring means you get better leaders for longer earlier on and at the cost of less Influence, which is surprisingly significant later. However, I can see Thrifty being preferable for very aggressive early play. Obviously Weak is the negative trait and that's pretty straightforward. This gives us a free point to use, so we can backtrack to Communal from earlier or go with Rapid Breeders. I find that Rapid Breeders is marginally more useful; it helps with sectors because they don't manage growth very well.
So my money is on Pacifist / Spiritualist / Individualist Moral Democracy, with Quick Learners, Enduring, Weak and Rapid Breeders. I'm pretty open to persuasion on changing around the Traits for Communal, Conformist, Charismatic, or Thrifty, I think there's stuff to be said for them, but I'm pretty certain that the government and ethoi are the best you can go with.
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