I've experimented a bit mostly on Prince and Monarch, and I've had a lot of success with 3 combos in particular:
Oxford + National Epic in a capital city
Ironworks + West Point (and a military academy, if possible; depending on civics and how far away I am from the next xp level bump, I might also want a Great General giving another +2 xp to bump up unit promotions another notch)
Red Cross + Heroic Epic (and another military academy, if I have yet another great general)
Why:
I used to put Globe Theater with National Epic as part of a standard GP farm, but lately I have been trying for megacapital games where I start off with 2 key cities: my capital (doubles as a super science city + great person farm), and a worker/settler farm. The capital builds a worker, settler, and then either stonehenge (if applicable) or the great wall, then it's off to the races: the 2nd city cranks out needed workers and expansion while the capital cranks out wonder after wonder after wonder (even the crappy ones, just for the Great People points), with the lulls filled up by building granaries, libraries, etc. with the occasional whipping until I get Bureaucracy. The 2nd city can be in a crappy location, by the way, as long as it has one or more megafood resources like corn or fish or something, since that city is going to stay below size 6 for a hundred turns or so as it's just a worker/settler farm. I finished a game recently where I built my 2nd city in a big desert area just because it had access to stone and gold (on desert/hills), but the city also had fish and a non-irrigable rice farm... and that was pretty much all I needed since it stayed at size 3 for seemingly ages (fish, rice, and gold mine).
Okay, I know what you are thinking; GP farm without Globe Theater? Solution: stuff as many religions as you can into your capital so it can build lots of religious buildings, build/trade for happiness-producing resources, build the Notre Dame, and if all else fails, whip a little more often than you have to. You'll usually have the Pyramids early on to help with unhappiness, anyway; Representation is great in combination with Bureaucracy+Mercantalism. That combo, along with a ton of religions in the capital + Great Library, Univ of Sankore, Colossus/GLighthouse (if applicable), Angkor Wat, Organized religion, stone, marble, industrious, Oxford, an Academy, a shrine (and market and bank), and a few more extremely useful wonders (the Spiral Minaret comes to mind) can generate a colossal amount of not just research, but production and gold as well, all while your research allotment never budges from 100% for a single turn as your gold pile easily climbs into the several thousand mark (especially with Spiral Minaret). Every single specialist I make settles in my capital unless it's more useful elsewhere (e.g., a great artist goes to a border city to help with my cultural, bloodless conquest).
As for the military combos, Red Cross units tend to be non-offensive units, so I don't need as many of them as I do the offensive units--units that will no doubt perish more often on the battlefield. The Ironworks+West Point timing, tech-wise, also works better for me than other possible combos. Red Cross always goes into a high-production coastal cities so that it can generate a few tag-along "healer" destroyers for my navy in addition to "healer" infantry.