Unfortunately I don't have MegaCorp so I only have the option between Science Nexus/Dyson Sphere/Sentry Array and the Ring World. The Ring World is basically to have somewhat of a feeling I reached the top, because I doubt I'd actually play much after I defeated the endgame crisis. But the thing about the Dyson Sphere does make sense, although I wonder how necessary it is to build that one first before repairing the Sentry Array if that will be the only energy-consuming megastructure I will build in the first place...Most of the megastructures use a lot of energy once completed, so if you are going that route, you will probably want to start with the Dyson Sphere. I wouldn't bother with a ring world myself. If you have Megacorp, I'd go for the Strategic Coordination Center, as it gives a big boost to fleet cap and other bonuses for your fleets as well. The matter Compressor is good as well. You'll be rolling in minerals with that.
A shame I don't have MegaCorp, cause especially that Matter Decompressor would've been useful to get a lot of minerals, my income of that dropped quite fast after I build some Arcology Districts on my Ecumenopolis. I'll probably repair the Sentry Array first, than build a Dyson Sphere and if possible repair that Science Nexus. That also reminded me that I want to build a Colossus, even if it doesn't really fit a xenophile, democratic UNE but I guess I can Palpatine it (and now that I wrote this, it should actually be a legit verbYou may want a Dyson Sphere and a Matter Decompressor. That way you have pretty much all resources covered.
The SCC, as @Bryartuck suggested, is always the one I go for first as long as my resource needs are covered for the moment. The Interstellar Assembly will make sure that the entire galaxy loves you unless you blow up their planets, but I'm pretty sure you need to build it in your home system for it to work (or so I've heard, so I do it that way just to be sure).
The Art Installation is great if you want to keep a lot of Unity Ambitions running, but generally you are able to do so without a dedicated megastructure.
Ringworlds can be your friend if you want to get rid of all agriculture districts on every planet you own, and the building slots can be utilised for whatever you need at the time.
And the Sentry Array is nice, but honestly I don't usually need to know what species X is doing at the opposite end of the galaxy. Though to be fair, once you own the L-Cluster no empire is too far from your borders, so that's a valid point.
Finally, the Science Nexus may come a bit late, but you only need to finish it, and don't underestimate the power of repeatables on economics and fleet strength shouldn't be underestimated.
That reminds me, the piracy is bloody annoying! I needed all my fleets to combat the Gray Tempest and Marauders so I had to leave my space unprotected, luckily only one system at a time spawned pirates but I think I lost a lot of energy/unity by piracy, it's also so annoying to split all your fleets in tiny bits to guard all of the space necessary, and having to merge them all back in one fleet is such a hassle.How to prevent Priate Spawns:
Do not have unprotected/insufficiently protected trade routes.
Or at least do not get current Piracy exceed maximum trade protection.