If you like fighting, don't listen to me. This is coming from a hardcore builder. Assuming: standard size, 70%continents, restless barbs, average other settings.
Personally I have no problem building whatever wonders I choose to on Monarch. Any higher difficulty and you have to get a little choosy, but if you are careful and are willing to forgo a little land, can net
all of the wonders after the ancient age. The key is prebuilds, tech lead, and 'breaking' the ancient age cascade.
I try to net as many of the wonders that last the whole game as I can [or that are useful/good sheild return], usually the Pyramids, the Mausoleum, and maybe the SoZ if I have Ivory. If you forego all lame military techs and go alphabet >writing >CoL >Philosophy you can get republic as your free tech and switch often before 1000BC. On monarch the AI wastes enough time on the other techs you will almost always be first to philosophy if you go for it. Goody huts can be about the only way an AI will get there too quickly.
Anyway, you should probably build your ancient age wonders in your capital, for lack of corruption if nothing else, plus it might help you contend for a 20k later on. Then the KEY is to prebuild sun-tzu's very early! If you are an early republic via slingshot, you should be in the middle ages 10-20 turns before the AI, assuming you traded with them very little. If you can net sun-tzu's before they even make it to feudalism, you're set. The timing of the AI wonders means they will have finished all the ancient age wonders before they get to leonardo's/sistine/Knights, netting you all of these useful wonders [dont forget your prebuilds for them!]. With your early republic, and maybe even the scientific trait, you can easily out tech the AI, which means you'll get those wonders first, b/c the AI doesn't know about prebuilds. All you have to do is stay either way ahead in tech or at parity, and you get every wonder that's left.
Some people say building wonders is a waste of sheilds, but on monarch or lower, a peaceful type really can build most of them if they want to...
If you get the wonders I do on monarch, you'll have free: granaries, barracks, hydro plants. maintenance free: banks, markets, stock exchanges, harbors, airports, commercial docks. PLUS: half price upgrades [worth it's weight in gold, literally], two extra content in all cities, double effect cathedrals, crusaders, a crazy hospital/cathedral/culture hybrid, +1 naval movement, lots of extra science in one city, low war weariness, two more free techs, the UN, nukes, etc...
Basically any victory condition you choose, except maybe 100k, is easy to reach, plus you are rolling in wonders.
The above has been used by me in almost all of my monarch level games, works great with a little practice. I think I'm wonder addicted
Edit: playing scientific civs might help you a lot, a scientific leader can net you a free wonder.