As Rome, if you're playing Earth18civs or some other map where you start out right next to your neighbors and know where all the others are, beeline Iron Working first while producing workers and barracks, then crank Praets while doing the worker techs and making the appropriate improvements. Otherwise, do the worker techs first, then iron working. Either way, once you have all the worker techs + IW, you should aim for Engineering, although it's okay to pick up some other stuff along the way, especially Currency. Once you have Engineering, currency, maybe Priesthood for the Oracle, maybe Feudalism for Vassalage (vassalage + barracks = 2 promotions for every unit as soon as it's built!), whatever, it's time for the race to Liberalism. First to discover gets Gunpowder for free, lol. Then aim for economics and music if nobody has beaten you to them yet - free Great People and whatnot. After that, it's Rifling, Assembly Line, physics, and ultimately Industrialism. You'll want to delay Physics for as long as possible even though the first to discover gets a Great Scientist, because its two prerequisites are Astronomy, which obsoletes your Monuments, and Scientific Method, which obsoletes your Monasteries.
Once you have Industrialism, you've won. Everyone who hasn't been overrun by your praets, macemen, musketmen, riflemen, or infantry will get overrun by your marines and tanks.
As Incas... I don't know. I've never played them. The basic liberalism-gunpowder-rifling-assembly line-industrialism path should work, though.