My thoughts on the matter:
The neinzul expansion is my favorite, very aggressively fun, emphasis on aggressive. However, it's a horrible choice to start with, because you can't counter wardens, enclaves, or hives the same way you can most everything else. The counters aren't that difficult, mind you, but they can wreck things in a hurry, especially if you can't spare any time and forces to respond. It's the last one I'd recommend you try out.
The spire expansion isn't that tricky - you generally remain very much in control when things get dangerous - but it is a nice challenge.
The zenith remnant? It's probably the first expansion I'd turn on. Dyson spheres, traders, etc- the factions generally aren't out to get you. Even the devourer golem isn't exactly out to get you so much as acting like a force of nature. However, the new ship types and especially AI types it can bring to the table can make things exciting in the hands of the AI. I also enjoy a lot of of the minor factions, but it's a bit of a toybox expansion, with things to play with, rather than necessarily against.
Stage One: Vanilla
For the first game, I'd suggest vanilla with astro trains AI Plot, and random moderate/easier AIs with random types revealed. Don't worry about finishing this unless you enjoy it. Instead, restart as often as you feel like, and get a feel for various AI types, bonus ships, basic defenses, how fast you can expand, etc. Don't put on the human minor factions yet - they'll just complicate things before you're confidently able to handle the regular stuff. Once you find some AI opponents you like, and especially the ones you don't like, go on to stage two.
Stage Two: Zenith
Now feel free to complicate things. Turn trains back off for the moment, but feel free to enable the all the minor factions available to you - except golems - you want that to be only on easy. While you're at it, up the difficultly of the AIs - if you were at six, try seven. If you were at seven, try 7.3. Take this as your opportunity to get familiar with these factions before you encounter them in a co-op game. The Easy Golem minor faction will help compensate for the higher difficulty you'll find. If you find yourself not liking something, feel free to restart and turn it off - you'll most likely find yourself despising the Marauders, though those pirates used to be my favorite minor faction. If you find yourself fascinated, feel free to carry the game through to the end, but don't bother restarting more than twice - after that, just enable the next expansion. I do recommend sticking to easier AIs TYPES for the moment. You might even want to go off of random.
Stage Three: Neinzul
If you're finding yourself comfortable at difficulty seven AI, or a bit bored over the course of a long singleplayer game, enable the Neinzul expansion - the minor factions and AI plot all tend to really spice things up and keep you on your toes, even when you have figured out how to fight the off with just stationary defenses. And when your stationary defenses fail, your fleet should be able to handle them a lot better than your turrets. If you're in a co-op game, you probably don't need the Neinzul factions enabled to keep things exciting. In a co-op game, your partner will provide both an element of uncertainty and direction when you're feeling overwhelmed by possible paths. I find a 2p game goes by a lot quicker than a 1p game for quite a few reasons. While you're at it, turn the golems back to moderate. Having them on easy defeats the purpose of inviting Neinzul into your galaxy. I suggest experimenting with the various AI types again, at this stage. Enable the zenith or human factions purely as a matter of taste. Having Golems on moderate will help reintroduce you to being careful about your power and resources in time for the next expansion.
Stage Four: Light of the Spire
By this point, you've gotten a feel for how all the minor factions play, and upped your difficulty level to something reasonable for your satisfaction. The spire content can be pretty drastic, so there are a few ways to approach this.
1). Keep your previous favorite game setup, just add spirecraft on medium, and AVOID the fallen spire campaign. The balance of difficulty should remain mostly the same, though spirecraft will remain a point in your favor. The AI will take advantage of some of the new bonus ship types to keep you on your toes, even though it won't use the asteroid ships.
2). Rebalance your game setup around exploring the fallen spire campaign content. This most likely will involve turning off Neinzul Wardens, Enclaves, Hybrid Hives, Marauders, and anything else that would be a horrible complication while you're trying to escort a plot point back to your homeworld. Meanwhile, feel free to turn up some other facets of the game. For me, I'm exploring the campaign with easy golems and spirecraft, but a starfleet commander and golemite AIs to keep things spicy, with a dash of Avenger plot.