If you want to get wonders and develop your empire, pick some civs that get Production bonus, choose Egypt, get lucky and find marble around your capital, pick Aristocracy from the Tradition tree or the Monument to the Gods pantheon.
The best situation would happen with Egypt (but civs like Russia, Carthage, Iroquois; that get some insta production bonus, are good aswell): they get 20% production for wonders as their UA; if they go through tradition, +15%; if they get the Monument to the Gods pantheon, +15% and if they get marble, +15%. In the end, they would end with +65% bonus production to wonders, getting them faster than normal, thus giving you more time to develop other areas later. You could also chop forests to cut some time.
It is important, though, to feel the game and understand when you should and should not go for wonders: if you find yourself on the middle of the Jungle, you would prefer to develop your empire first, as the production wouldn't be enough and you would end with a GL taking 37 turns to be built. During that time, you could develop your production with water mills, workshops and mines instead, which is way nicer than spending a lot of time trying to build a wonder and see another civ get it one turn before you. Also keep in mind that you can always conquer other wonderful cities.
Try not to rely your strategies on wonders, because they won't work every time. In some games it might be a great idea to build the Great Library, but in others, it would be better to develop your empire instead of trying to compete with A-Wonder-Every-6-Turns-Russia