Let me lay out some theories I've had kicking around in my head about how to set up two civs to complement one another. (Ah Thanksgiving, lots of time with relatives to spend thinking about Civ stuff.) I'll preface this by saying that this is all theorycrafting, and as someone who's not playing in this game, you guys can opt for something else entirely.
Civ A (our potential Rome pick)
This civ focuses on the economic and production side of the gameplay. The goals for this civ are to make sure that the team stays current in military power, along with maximizing gold generation for the team to share. If this ends up being a Rome pick, this civ will also lead the way in culture for the early portions of the game and clear a path for Civ B to unlock the early civics. These are the districts that Civ A will want to focus on:
1) Commercial/Harbor districts (one per city, preferably Commercial districts)
2) Industrial/Encampment districts (some mixture of both)
3) Campus districts (every team needs science)
4) Theatre districts (as necessary)
Civ A also has the goal of getting one city with Encampment/Commercial/Harbor/Industrial districts so that both players have the option of running 1 food / 5 production trade routes there, a setup that's great for most everywhere. Depending on the civ that gets selected, the team can plan out which tech and civic boosts for this player to select. This is the more straightforward of the two roles, playing the game mostly like it would be played in a solo venture. Money and production and military are the main goals here, making Rome or Germany very good selections.
Civ B (our potential China pick)
This civ has the goal of setting up an early religion, then concentrating on research and cultural output down the road later. If we are able to get a China pick on the second swing through the snake draft, then it will also have the goal of landing the key early game wonders. Here are the districts that Civ B will want to focus on:
1) Holy Site district (every city of Civ B gets one)
2) Commercial/Harbor districts (one per city, preferably Commercial districts)
3) Campus districts (every team needs science)
4) Theatre districts (as necessary)
This civ should not be building Encampments, and only the minimal number of Industrial districts needed to ensure everything gets the regional factory boost. Our goal here is faith output and then science/cultural generation. Each city still wants a Commercial or Harbor district though, simply because money is great and trade routes are awesome. Production output will necessarily lower, but that will be countered with stellar economic output of beakers and culture.
For a China pick, the first goal is getting Stonehenge and landing the first religion. If Russia is the pick instead, then use cheap Lavras to land the first religion. Take Defender of the Faith immediately to make the team a prickly target that no one wants to fight. Civ B has the goal of generating faith and using it to spread the religion to both teams. That means a Holy Site in each city with attendant shrine, temple, and worship building. Pretty much any of the worship buildings are good here (especially Wats or Meeting Houses), and that belief can be evangelized later, potentially with China getting the two apostles for free from Mahabodi Temple. For the founder belief, the one that grants +2 gold per city following the religion would be the easy choice. The harder pick is the follower belief, and that's what should be chosen immediately along with Defender of the Faith. I suggest one of two things: either the new Choral Music which grants culture equal to the faith output of shrines/temples, or Jesuit Education. Probably the latter, because the best use of faith is to use it as a way to purchase other stuff for free. For Civ B then, get the first religion, get Defender of the Faith and Jesuit Education, then build Holy Sites and spread the religion to both players, using faith to purchase science/cultural buildings one the faith generation gets going.
A China pick means a guaranteed Pyramids/Colosseum/Petra, and then any of the other early wonders if desired later on when they become super cheap. With Autocracy and the policy card that grants +15% to Ancient/Classical wonders, one builder practically equals one early game wonder. Smart targeting of the important ones, plus a powerful early religion, should snowball the team significantly ahead. At that point, it's a question of whether to try and dominate the other teams by force or go for something offbeat like a cultural win. It might be doable under these settings here, where aggression seems difficult to pull off.
Anyway, just some thoughts bouncing around in my head. I also like Rome or Germany for the first pick, and then China or Russia for the second one.
Though as none of our games have really gotten anywhere close I don't think that would be realistically tenable....
I'm feeling like first pick I should really just take a strong all-arounder, Germany or Rome, and then figure out where to go from there.
That's a really great outline for division of responsibilities. I would definitely agree that following that type of plan, Rome/Germany and then China/Russia would be ideal. But since we're apparently seeing starts first anyway, let's see if we end up getting one that will change the weights any.