I just checked, I did the default start, so my Advanced AI is on, but Advanced AI neighbour is off.
I see. Depending on the other settings and luck, you could end up with at least one advanced AI as your neighbor even if you didn't "force" it. You could remove Advanced AI for the first few games if it's causing you more troubles than it's worth while you're learning the new mechanics.
Still, even there, you'll probably have to start over a couple of times to get things right. I know I did. Even after more than 150 hours in since Le Guin, I'm still learning some new stuff and I'll probably keep on learning. This game has a lot of sub-systems, mechanics and/or micromanaging and as such, you cannot get to know or even try everything on your first couple playthrough, unless you follow a guide/video maybe (which I mostly never do). If, like me, you play on Ironman, it means that you simply can't go back and try things differently if you made a mistake in the last few years: You'll have to power through, or give up...
While the AI is sub-standard at best (even with the latest patches which reworked their priority and made a few tweaks), the game itself is more complicated than, let's say, Civilization (even if we can't call Civ a barebone game). Even if the AI is kinda dumb, they get massive boosts with each increase in difficulty level, and well, they could overpower you unless you prepared properly and tried to limit mistakes to the bare minimum.
So, to recap :
1) Use a couple of Construction ships. Personnally, I generally use two early on, unless I'm using a Xenophobe species which means that I can set starbase every few months (in which case I would probably use 1 or 2 more) instead of every two years or so.
2) Always set up mining and research stations in your systems. There is an upkeep cost per station (1 energy per month, I think, except in the case of energy mining which has no upkeep), but it's easily offset by the ressources/research you're actually getting.
3) Set up trade routes. Ideally, you'll want those protected as soon as piracy comes into play (which isn't the case early on). Use corvettes and/or build other stations: Pirates never attack Citadels, so you don't need to protect thoses. And also, I find that individually linking each spacesport is better when it comes to creating a single trade route. If you let the game choose automatically, you'll often end up with a couple of different trade routes and it makes everything pretty hard to defend against piracy. Creating a massive "single" trade route makes it easier to defend, but it will be more targetted too. It's a tradeoff I guess.
4) Find a choke point for each AI, especially if they're not sympathetic to your cause. Build a starport and build these Gun Battery/Missiles/Hangar Bay modules. It will significantly increase the starport power. Build defensive platforms on these ones. You'll be able to set up anchorages on your other starbases, but your choke points are, IMO, very important. Last game (Admiral difficulty), I had the entire galaxy against me (Pacifist Xenophobe... like why would you hit me, I'm minding my own business?) : Two federations consisting of 3-4 empires each allied themselves to either humiliate or conquer my territories. I had a meager fleet worth 75k (23-25k per unit). They sent two full federation fleet of 45-50k each, and 6 or seven 10-15k fleet from their individual fleet. Let's say I was overpowered when it comes to raw power (75k vs maybe 200k). Thankfully, I had a 50k fully upgraded Starbase with 23 or 28 Defensive platforms on each chokepoint and even if they swarmed, they didn't come all at once. I almost lost these systems, but as they had to come through this one to even hit me, I gradually reduced their fleet to ashes and claimed a few systems to split their territories in two after the end of the war. They went downhill after that and left me alone. Without my defensive starbases, to even come close to what would have been needed to defend against a fleet that huge, I would have to have double the fleet power, which would mean at least 150-200% increase in ship's upkeep (as I was already over the cap by a significant amount). My economy probably wouldn't have recovered if it were the case as things were running pretty tight.
5) Build Autochthon Monument (and their upgrade), ideally one on each of your planets. Ascension perks are pretty much needed, so getting your Traditions fast is not wasted IMO. After that, you'll be able to pick another building if you're getting more Unity than you can spend on edicts.
6) Don't mind the Administrative Capacity too much (Empire Sprawl) and try to get your fleet up to your Naval Capacity every time. It will be costly in upkeep, but you'll be ready if they ever try something funny. AI tend to attack those who are weaker in raw power, so if your fleet is similar to theirs, they might be tempted to look the other way (unless they really want your territories). That being said, purifiers/assimilators and the likes won't really care, unless your fleet really is larger than their.
