Well, I consider this run lost – alien armies control over half of Earth, their servants another 25%, they are methodically glassing all my stations and colonies, and I'm technologically way, way behind them. Key takeaways from this (ie. mistakes I made that cost me the run):
1. Don't let Servants get their hands on any superpower. Everyone else is fine, but not Servants. They probably get some manner of a tech boost from the Ayys, and go super aggressive once aliens land, basically double teaming everyone (and you can't do anything about it because they ally the aliens). In my game they took China, and it was impossible to oust them from there. They also like to start nuclear wars. Remember: if nukes start flying, Servants win, everyone else loses. Doesn't matter who wins the actual war.
2. It may be tempting to focus all your research on projects, letting the AI factions spend their points on global research. This is a bad idea. The way the AI picks global research is practically sabotage. Instead of, for example, pursuing one line of weaponry to get to some good guns, they will pursue EVERY line of it, so you will have choice picks of all the different flavours of garbage guns. Don't worry too much about "wasting" points on global research – a massive number of the research projects are practically just filler anyway. You should focus on the ones you actually want, even if they take assloads of time to get, rather than going for the cheap but useless things.
3. Your faction rivals are mostly pests (save for Servants, who look like pests up until the time aliens land) and not your real enemy. Don't waste your time trying to sabotage them or fuck them over, you're just wasting resources your should reserve for the aliens. That said, if they get their grubby hands on something good (countries, or space stations in good positions), don't hesitate to go and grab it from them. Even if their relations hit rock bottom, they can't actually do all that much to you if you're handling the country micro well.
4. Funding is useless at start, but becomes increasingly important later on. Larger income = more mining colonies you can support to get their resources. It's also good to have cybernetics for your counsellors, and those are expensive. Selling resources works in a pinch, but is not sustainable – you actually need the resources you mine, you can't just keep selling them. Why? Because decent ships cost a LOT of them, and you'll be wanting to build a lot of those. Similarly, it's never too soon to build mission control. Bigger ships cost a lot of it. You can sort of get both by building space stations, but be aware that eventually, the big bad alien will stop ignoring you, and will come to take them out. And not just one or two, he'll go and fucking purge them from orbit. You better either have the muscle to actually defend them, or not be reliant on them in the first place.
5. Armies are important. Grab them and slowly build them. Having a high level of your military is, likewise, important. The aliens will come with Quality, not quantity, so you best be able to overwhelm them. Ignoring them leads to them sending in more and more of their high quality troops, and then you're kinda fucked. Best to be ready to squash them right when they land with an overwhelming force.
6. There is a massive difficulty jump when the aliens arrive. Be ready for it. Don't get complacent just because you're doing very well compared to the other factions – as I've said, they're just pests.
7. Remember that your armies are useless if they cannot get to the enemy. Having a navy attached to your army can be extremely important, especially if the aliens land on another continent
8. Consider having a counsellor become a fulltime adviser of your "main" country. You don't actually need every councillor for the country micro too often, and getting a 25% bonus (assuming you hit the skill cap on the relevant skills) can be a pretty powerful boost for it.
9. I will reiterate: avoid nuclear war at all costs. There is no recovering from it. You'll be gimped for the rest of the game if you let it happen, and it doesn't manner where in the world you are. The ecologic fallout of it ruins the economy of everyone in the world (and the nations involved are forever ruined. Not only is their economy down the drain and their population decimated, they will also start to lose population from then on, and very quickly too).
10. Faction objectives ask you to do expensive research. This research gives you absolutely nothing (well, okay, it unlocks a couple techs, but they're mostly just 'nice to have' rather than something to beeline for), but eventually leads to unlocking a new kind of resource (that you'll need to build the best ship parts and stuff) and that you'll be getting from wrecking alien ships (I assume. I lost the run before I could test this out, but it seemed likely). Plan accordingly.