I only play on Apollo and even though the wonders aren't nearly as big of a deal as they were in Civ V, I'm thankful that it seems the AI doesn't manage to monopolize them as easily as they did in V.
I thought of my top 5, but I think I'll do top 10 just because I was thinking of honorable mentions and it might as well just be 10 anyway.
1. Genevault
For the reasons people already said, you can get it early and I like it helps you compete with how fast the AI seems to manage to grow their cities and getting it denies them from being able to get even bigger faster.
2. Ectogenesis Pod
I have a bad habit of spamming farms even when it might be better to use generators or extra academies in some cities, so +1 farm food is great for me, even if I'm not going purity. I usually try to get both Genevault and Ecto Pod before the AI can grab them so I can get my cities as big as possible.
3. Panopticon
Since I like domination best, +1 unit sight is great for everything. Plus as people have said it's pretty cheap to build and comes relatively early. This is one I always try to make sure I get, even if I don't plan on fighting a lot.
4. Deep Memeory
I should probably put this below Promethean but I tend to give it some extra priority in the late game since the 2 virtues usually help me get to the bottom of the Might tree (which I get after I got what I needed from prosperity and industry trees already) to either get the 50% unit maint reduction and 10% combat boost or get the +50% resources. I almost always go domination and either way it's great to have a bigger and better army late game since. Plus the AI is usually pissed off at me by then, even if I'm not doing domination. It might be higher if it wasn't so out of the way, at least if you're not going Purity.
5. Markov Eclipse
I'm surprised nobody's mentioned this one yet. If you plan on fighting a lot, like I end up doing, it's really nice to have this to speed up promotions significantly. When defending or moving in to attack under heavy fire, using heal instantly can also mean the difference between a dead unit and one that can keep attacking or defending. Needing less attacks/hits to get that heal can be a nice bonus for keeping your defensive line alive to soak up more attacks or allow an attacking unit to keep going/hold position. I don't prioritize this as much as the first 4 wonders but it's noticeable when you have it. This + the might virtue lets the promotions roll and/or your army stay alive longer.
6. Master Control
As the list goes down these each become less of the wonders I really prioritize, and Master Control is one I probably don't focus on that much, but I probably should since it's pretty nice to have. This is especially useful with how good academy spam. In the same way worker speed % helps you construct the improvements faster, this helps you get workers on site faster to get started. If you usually have a small army of workers like me the benefit from this thing is certainly noticeable.
7. Crawler
Bytegeist would of gone here, but lately I've been trying to make the Crawler more often and it's pretty nice. I actually feel like an idiot after seeing it mentioned here about how it helps with the affinity victory wonders. Somehow I never had that even come to mind, and thinking about that benefit makes this move up from what I would of had it at. My main problem with it is that it's from a tech that's usually out of the way for me, plus it's a bear to build in itself. But if you wanna go for stuff like Deep Memory or Xenomalleum(aside from victory wonders), since you can get the Crawler easily before those, it's helpful. Also almost worth getting if you're the PAC for super fast wonder building. I almost always play PAC mainly for the worker speed bonus, but Jesus Christ the PAC wonder % bonus + industry wonder % virtue + the Crawler is hilarious. I've had Deep Memory be like 12 turns, and victory wonders be similar.
8. Bytegeist
I actually don't get this one very often, since where it is on the tech web I usually don't go for soon enough before the AI can make it. However since virtues are so strong, and playing wide is so common the -15% virtue cost is pretty nice to help mitigate your expansion from slowing up your virtue progress as much.
9. Precog Project
After I get the tech of Academies, if I'm going Supremacy I'll usually go for the tech with this + the affinity boost right after. Even if I'm a different affinity, I'll try to swing back around to try and get it if it's not been taken yet. This thing is both cheap and a really nice benefit all around. It helps both in defending your own territory, and if you're attacking an enemy with how taking cities and converting the enemy territory can give your units the bonus for some of the time as they advance. It's also nice to keep it out of AI hands at the least, so it's not harder to attack them instead.
10. Xenomalleum
I've actually almost never built this thing, which is a big part of why it may seem really low, but I still see why it can be really good. Personally, I don't have many money problems in my games, and unless I have lots of tundra I don't use many generators, even when I have lots of academies up. But I still see why a lot of people would like this one if they do use lots of generators. I also don't tend to get to that part of the tech tree until very late and I don't put any priority on getting over there. I'll have to try generator spam sometime though, with this plus the other techs that help generators and see if they're really that beastly. It's just a strategy I haven't tried yet.
Honorable Mentions:
Even after 10 good wonders, I think an honorable mention would be Memetwork. I never really put extensive focus on culture in a city like I do science, but this is nice to have if you wanted to do that. Like the Xenomalleum it's just something I haven't really messed with much yet.
The Drone Sphere can go here since it's kind of similar to the Precog Project. It's not quite as good as the PP in my opinion and it's more expensive. And since you always want to get Academies the PP is a bit more natural to go for. Plus even as a different affinity Supremacy affinity is nice to get for the sake of the free roads/rails at rank 3. The Harmony affinity with the DS is pretty useless for anyone else.
Cynosure is also kind of an honorable mention but it's one of the slowest to build and 1 extra veterancy level isn't that big of a deal. If this game's promotions worked like Civ V and had stuff like logistics, +1 range, etc then maybe. I can only really see the value on the super units with an extra +10% to their like 100 strength, but still kinda meh. If it was a lot cheaper it might be worth it.
Don't really need to put much comment on the worst wonders, since they really speak for themselves.
1. New Terran Myth
2. Ansible
3. Daedelus Ladder
4. Nanothermite
5. Mass Driver
All of these either add nothing but minimal yields to culture and whatnot and provide nothing else, or have a pretty useless effect. I didn't put the city defense or production wonders as the worst just since if you had to make me choose I'd rather gain city defense/HP or +6-9 production than a tiny bit of culture or food and nothing else. And good lord I may have went on too long with this post.