I really don't get why the Great Library and Petra are held in such high regard.
The great library is essentially a GS point, a free tech and 1 gpt for 110 hammers. The free tech to me doesn't seem that big of a deal (and a free SP much better), scientists are really easy to come by when you need them most in the late game anyway, and 1 gpt (saved from maintenance) is a meh. Please enlighten me!
It's because, like the GSes in vanilla, you can use strategies that make this situationally powerful, by landing the right tech at the right time - in vanilla Philosophy was the go-to, but this is now less important because Research Agreements aren't unlocked until Education and are in any case harder to exploit. To be honest it's probably a case of people overvaluing the GS now based on what they used to do with it in vanilla. I'm guilty of going for it by default most games, since Pottery is strongly favoured as the first tech - it's good but not a huge boost. You also forget that it gives you a library, so its 110 hammer cost is effectively discounted - aside from time there's no particular reason not to build the GS instead of a library when you get the ability.
Petra seems okay, but what I don't get is how you can possibly take advantage of it. If you've got a start with enough desert for Petra to be worthwhile, surely your production would be abysmal and you wouldn't be able to build it?
See my above. It's not for fixing a bad start (you don't get it until Currency), it's for enabling you to plan and settle a productive desert town.
And I don't even see how a base 1g, 1f, 1p is *that* good anyway; a plains start isn't held in much high regard and, unless I'm missing something, isn't that essentially what Petra provides?
You're missing the fact that not all desert is created equal. You can get good resources in desert, and desert hills can be mined - Petra makes for good production cities. Desert Natural Wonders also get the bonus, and settling near Natural Wonders is often a trade-off between getting that bonus and landing in unproductive terrain. But probably most importantly, it gives a gold bonus to
every desert tile you work, and gold in the early game is in short supply. Also, don't make the mistake of assuming that because it has most effect in cities surrounded by desert, you need to settle only in the middle of deserts with no other tiles.
But most of all you need to look at it in context. The question is not "What is the best Wonder?", but "What is the best Ancient/Classical Wonder?", so comparisons with other Wonders of the same period are invited. Given the right tiles, it gives you the gold bonus of the Colossus. Plus the effect of a Lighthouse, albeit in desert rather than coastal tiles in both cases. Every desert tile gets +1 production (including that wheat you're using just to feed your people), which has no analogue in other buildings/Wonders at that stage in the game. And this is the early game still, so +1 of each of those is a meaningful bonus that can drastically increase production times, growth and income.
Oh yes, and on top of that you get a free amphitheater - a very nice nod to the fact that there is a Roman amphitheater in Petra.
Given the right conditions, there really is no Ancient/Classical Wonder that comes close to Petra in power, and this shouldn't even be in question - where deciding whether it's the best Wonder comes in is in determining how reliably you can exploit it.
