IMO, it's Stonehenge, Great Library, and Hanging Gardens.
Hanging Gardens, Petra and The Oracle. Pretty much in that order.
Stonehenge is very definitely optional, and is if anything worse now than in G&K due to improvements to Piety. Stonehenge + Piety is good once you get a religion, but still fundamentally more limited than the above, all of which provide bonuses that set you up for the long haul and work well with any strategy.
Great Library is now a very good pick for culture victory, but its limitations as a science Wonder are the same as ever - its build time relative to the Library is so long that you will usually get at least as many beakers just by building a library and focusing on food, and you're forced to go for an early tech because the Wonder is taken so quickly if you don't. Which all might be fine, except that you usually want to build this instead of a Library and so if you're beaten to it at the last minute you've actually lost beakers. Its much too early in the game to affect your science ranking significantly to boot. Beeline as Babylon (GS points) or France (theming bonus), otherwise there are definitely better options. Even Korea doesn't need it since the science boost for building the GL is exactly the same as the boost for building a Library.
As a fourth best Ancient/Classical Wonder the Great Lighthouse must get an honourable mention - the lighthouse is now a much better building to have, free buildings from early-game Wonders are more valuable now that early gold is limited, and most civs now seem to have coastal biases to help make use of sea trade routes.
Stonehenge? That's an odd shout for me. Correct me if I'm mistaken, but +6 ... that's it, right? Desert Folklore would get you that.
Only if you have 6 pop working desert tiles that early in the game. Stonehenge has one purpose - to get a quick pantheon. Desert Folklore won't get you that (though Tears of the Gods will). It's just no longer optimal for that unless you have reasons not to take at least the first two Piety policies early.
The Great Wall makes you virtually invulnerable (at least as long as the battle AI is remains "special"),
AI limitations are the key reason the Great Wall is mostly useless. If you can defend, you can do it anyway. If you're in a position where you will lose a city to an AI - i.e. you don't have an army - slightly restricted movement for attackers is not going to give you the time to build one. The GL ability has remained similar through most Civ incarnations, and wasn't designed with Civ V's ranged combat in mind in particular, which makes the reduced mobility around your cities much less relevant anyway.
Of course you can build it to deny it to an AI, but then the AI is worse on defence than it is offensively, so an AI with a Great Wall isn't much less vulnerable than one without.
but Petra in particular is a must-have (assuming you need it.) Desert is a graveyard otherwise.
You don't want many basic desert tiles with Petra anyway - you want resources, hills and oases.
The three best wonders? Petra, Temple of Artemis, and Hanging Gardens.
This is a good list too - Temple is indeed very good. I'd still edge The Oracle ahead for versatlity and the Great Scientist point.
Without a tech ruin or maybe Solomon's Mines GL seems to be pretty much impossible to get on anything past King
With planning it's possible consistently on Emperor unless you have a poor production start. It's also slightly easier to get in BNW generally because AIs no longer start with Writing (as they did before) and they tend not to prioritise it as a tech. On the other hand, they don't prioritise it for a reason - a library isn't immediately useful because a city will be too small to make use of it, and now there are competing superior options such as Animal Husbandry, Sailing, and in some contexts Bronze Working. So you have to beeline an otherwise non-optimal Writing path to get it.
On Immortal you need a bit of luck with starting location, as well as to prioritise it, but it can be done.
The best or the best that you can get?
If we go with the latter, the Hanging Gardens are straight out of the window.
And on Immortal+ they basically automatically become Oracle, Petra and Stonehenge since these are the only ones that stick around except the somewhat sub-par Pyramids and Great Wall.
EDIT: Okay, Mausoleum would fit there too. That's usually obtainable. Temple of Artemis is easier than Hanging Gardens, but still a challenge to get on Immortal most of the time.