Here is the build start of a typical "culture win" playing as Elizabeth at emperor / immortal on marathon speed and a continents map with everything set on normal. You don't have to go for a culture win, because these wonders will help you enormously in whatever victory condition you want.
The boost benefit you get from certain wonders is huge and it helps enormously if you plan on building the right ones that will fit in with whatever strategy you are following. I am explaining the build strategy, as you need to build / research in a certain order, as the wonders have prerequisites conditions, and following this build order will help you to beat the AI to them.
Capital - build 1 or 2 warrior or fishing boats / research bronze
Start worker / whip half way / research masonry
Start worker /chop
2 x workers chop settler / research one health + any nearby luxury
Great Wall = chop / research roads then Mysticism and Meditation
Build monument whilst workers link up resources and road to city 2
City 2 has to have it's fat cross in a very good location, not necessarily on bronze / horses, as it's going to be one of your 3 culture cities. Build / chop warrior + monument, then have it build a settler.
You now switch back to your capital, and build / chop "The Pyramids". You don't need stone if you have a lot of forest, but it helps. Meanwhile research Polytheism and Libraries, and when the "Great Wall" pops a Great Spy settle him in your capital to get the science boost.
Once City 2 has produced it's settler, have it produce a worker.
You now need your third "Good" location for your final culture city, and needless to say it is going to have to be close to horses or Cooper, if you don't already have them. Again have it build / chop a warrior and a monument.
OK, now this is the tricky bit, because in the next few mins you are going to get "Aesthetics" and the choice of 3 wonders to build, and you can't mess it up.
As soon as the Pyramids is built switch to "Representation", and that spy you settled will really start earning his keep. N/B: Don't forget to free up your capital to grow again, as it will be stagnant from a health / happiness cap by then.
So what do you want to build / chop from Aesthetics?
Well marble / gold / ivory will build them in double speed, so see what you have, but you can build / chop all 3 without any special resources, providing there are forests nearby.
The 3 monuments you built will now allow you to go for the "Statue of Zeus" but I personally prioritise the "Parthenon" as it speeds up GP production and the "Shwedagon Paya" because it allow all religious civics and if I am going for a culture win, then I want "Pacifism" as again it speeds up GP production. I also want the "Shwedagon Paya" in case I need to switch to "Free Religion" a bit later, should there be hostile AI nearby who have a different religion.
You should be able to comfortably build / chop / whip 2 of the wonders, but you may need the "Pyramids" to pop a Great Engineer if you want all 3.
If it does pop a "Great Engineer" then I won't use it on the "Statue of Zeus", because after I have discoverd Aesthetics, I go straight for Literature, so that I can Build "The Great Library".
Once I have Literature I will then research Mathematics and Music to give me "The Sistine Chapel".
Deciding which wonder to build in which city is important, because different wonders generate different types of GP points. For example, in the above scenario you don't want the Great Library in your capital, because it will then be much more likely to pop Great Scientists, rather than Great Engineers or Great Spies.
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If you follow the above, then you will have a tech lead from Aesthetics onwards, so the AI will start to pester / threaten you to trade those wonder techs, whilst you are still building the wonders, so only trade them when you are ready. If you should trade them to early, then you risk the AI building the wonders.
The power of having any Govt civic (Pyramids) and any Religious civic, (Shewdagon Paya), that early in the game is huge, and you can mix and match your civics to fit whatever victory condition you want.
Likewise the combined power of the Parthenon and Pacifism to speed up GP production is huge, and your cities will pop GP faster than you know what to do with them. Last but not least, if you do go for Representation, then think very carefully about what specialists you are running in each city. If a city has wonders in it that are going to pop say a "Great Artist" then running 2 scientists in that same city for any length of time will almost certainly cause it to pop a "Great Scientist", rather than the "Great Artist" you actually want.
You can rush GP production by running specialist temporarily in a city to increase the GP points being generated by that city, but keep an eye on the slider that tells you the GP %. A 30/70 % split is reasonably safe to pop the GP who is at 70%, but you can get a surprise GP if it's higher.
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Once you have the above wonders + the choice of civics + ultra fast GP production, then you can play whatever game you want, because you now have some major advantages over the AI, as follows:
1) You have destroyed any chance of the AI getting an early Culture Victory. and deprived the AI of getting a big boost from early wonders. If you don't build these early wonders, then the AI will, and they will then have even more advantages than they start with.
2) The wonders you built will give you huge and strong cultural borders, and no AI will be able to encroach on your territory using culture. In fact if any AI has a few cities that are located to close to you, then they will flip to you. Even cities belonging to the highest ranking civ will flip, if they are to close.
3) Your tech lead allows you to trade for anything you didn't research, and the "Great Spies" from the "Great Wall" can steal anything else that you want.
4) The "Great Engineers" from the "Great Pyramids" help you instant build wonders.
5) The ability to use any govt / religious civic speaks for itself, as the AI has to discover loads of tech before they can catch up with you.
There are many, many other advantages from the above start, but life's to short, and I'm sure you can figure them out for yourself or will discover them when playing the game.
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To experiment with the above - save before you discover "Aesthetics" and treat that particular game as a training exercise. If you can get "Shewdagon Paya" and the "Parthenon" and the "Great Library" then class is ended, and you can go and kick AI bottom in a proper game. I suspect you may have to replay the game from your save point a few times to nail it.
Going for Mathematics + Music is only needed if you are going for a culture win, so once you have the "Great Library" you can tech wherever you want, and use whatever govt / religious civics you want.
Remember that you can change govt type instantly during a Golden Age, and don't forget about "Free Religion" if you want to keep certain religious AI nuts off your back.
Hope the above helps - best of luck.
Regards - Mr P