Good Culture Wonders
There is a good summary table at https://civilization.fandom.com/wiki/List_of_wonders_in_Civ4#Ancient that I would study carefully. You should have Wonders that you are aiming for, and get the required discoveries in place to build them. Wonders have prerequisite discoveries. For instance, if you wanted to build the Temple of Artemis, you first have to research Polytheism, so pay attention to your research program. If you were to go this route, bear in mind that if you are the first to discover Polytheism you will be the founder of Hinduism, so if your strategy is to get a religion and found a Holy City as well as build the Temple of Artemis, you should immediately bee-line your research to Polytheism and kill two birds with one stone.
Also, the effects of most Wonders apply to the city in which they are built, so you want to build them in your Culture cities.
Ancient
I usually skip the Ancient Wonders because I prioritize building up my Empire at that point. You can get 8 Culture from Stonehenge, Oracle, and Temple of Artemis, and 6 Culture from Pyramids and Great Lighthouse. The Great Wall only yields 2 Culture and is mostly defensive. I don’t find it worthwhile for me.
Classical
The big three here are Mausoleum of Maussollos, Parthenon, and Statue of Zeus. All three of these yield 10 additional culture, additional Great Artists points each turn, and other benefits.
Medieval
I don’t always grab the Classical era Wonders, but by Medieval I need to get cranking. For me the top is Sistine Chapel, combined with a State Religion. Notre Dame and Versailles are also good, but as a pure Culture play a second level to Sistine Chapel. Spiral Minaret has less Culture added, but gives a nice financial boost to Empires with a State Religion. That is not to be despised.
Renaissance
There are only two Renaissance Wonders, Statue of Liberty and Taj Majal. Taj Mahal is slightly better on Culture, but the added free specialists from Statue of Liberty makes it about equal. I’d call this one a toss-up. Those free specialists can help your Military and Science cities.
Industrial
Broadway is the one here.
Modern
Hollywood and Rock ‘n’ Roll are the ones here. Neither yields added culture points directly, but they give you a 50% boost to the points you are already generating.
Good Culture National Wonders
Remember, these Wonders can be built once by each player, so you are guaranteed to get them if you want to build them. However. National Wonders can only be built 2 per city. So you need to strategize which ones you will build where. Since you are not in competition with other players to build these, don’t feel rushed. Figure out the best way to maximize your return on investment.
Ancient
Nothing in the Ancient era
Classical
Globe Theater and National Epic are the best ones here. Globe Theater gives you 6 additional Culture per turn, plus turns three citizens into artists. National Epic gives you 4 additional culture per turn plus doubles your birth rate for Great Persons.
Medieval
There are no Medieval National Wonders in the game.
Renaissance
Hermitage will double your culture in the city you build it in.
Industrial
There are no major Culture National Wonders in this era.
Now, just because there are only three major Culture Wonders, do not neglect the others. You should also have Science and Military cities that can use boosts, so by all means build those wonders in the appropriate cities. As for where to build the Culture National Wonders, I would recommend building the Hermitage in the Culture city that is lowest in Culture output so that it gets the big boost. Remember you need to get all three cities across the line to win.
Good Science Wonders
Ancient
None of the Ancient wonders are crucial, in my opinion, though of the bunch Oracle gives you a free tech and a boost to getting a religion. Remember that religion can help boost your Science, so this is not in any sense wasted effort. But in practice, as I said above, I often skip Ancient wonders altogether to focus on building out my Empire.
Classical
Great Library is #1, followed by Parthenon because of the boost to Great Person points.
Medieval
University of Sankore is best here. But you can use a Religion-to-Boost strategy that would make Angkor Wat and Apostolic Palace good choices as well.
Renaissance
Statue of Liberty for the free specialists. Put an extra scientist into each city.
Industrial
Kremlin is best here because it reduces the cost of hurrying buildings.
Modern
Space Elevator is crucial here for building your spaceship. But don’t overlook Cristo Redentor for being able to swap policies without the anarchy period.
National Wonders
Remember that you can build all of these, though in practice you probably won’t because of competing demands. But the key ones are National Epic (for the boost to Great Person Growth Rate) and Oxford University. If possible, build Oxford University in the city with the highest Science output since it doubles the output of the city.
Good Military Wonders
Ancient
Great Wall #1 for getting more Great Generals. But Pyramids is also useful for giving you all government civics.
Classical
Statue of Zeus will help demoralize your enemies, Chichen Itza builds your defense, and Parthenon boosts Great Person Growth Rates.
Medieval
Consider Hagia Sophia for rapid building of roads. Conquest goes a lot smoother when you can get your units to fight faster than your enemy can. Apostolic Palace can give you a production boost, but on balance probably not enough unless your State Religion is widespread throughout your Empire.
Renaissance
Statue of Liberty for all of the free specialists.
Industrial
Pentagon is the obvious first choice, but don’t overlook Kremlin for the Great spy and the lowered cost of hurrying buildings and units.
Modern
Three Gorges Dam would be my first choice for the production boost, but Cristo Redentor is good for changing civics without the anarchy period.
National Wonders
Again, you can build any or all of these, but in practice you usually need to choose. Top would be the Heroic Epic in the Classical period, though I would also consider National Epic for the Great Person growth points. In the Renaissance period you would want to build West Point. Put it in a city with high production and lots of military buildings to multiply the bonuses. In the Industrial period I would go with Ironworks first, and if possible put it in the same city as West Point. That would let you crank out lots of units with high stat levels. In another high production military city I would put the Red Cross so that damaged units would heal faster.
Summary
These are all simply general suggestions. The strategy sites like the Civilization Wiki and Civ Fanatics, to name just a couple of the better known sources, will have a lots of discussion of strategies, and if you want to be a really successful player they go way beyond what we have discussed here. But remember that gaming is supposed to be fun. Get the game, try it out on the easier difficulty levels, and play around with the ideas we have outlined here. You just may get hooked. Civ 4 was a great leap from the earlier versions of Civilization, and many players still consider it to be the best in the series. So it is worth a little bit of your time to get to know it.
