War early. War often. If you don't, they will, so you might as well be ready for it. Sitting Bull is (no surprise) a good leader for this map, because you can get those Dog Soldiers out uber early. If you play without world wrap, develop a safe corner if you can, then work from there. If not, then expect potential war on any front. Early on, I liked to build the GW and just build military to take out the AI, but that was before I learned how to expand quickly; now, the Spy points just aren't worth the security. Remember that all the happiness resources are in the mountains, even though all your enemies will be on the plains-- managing this split in priorities is the hardest part of the map, for me. With enough population, you can develop some monster production cities.
Well, I'm close to finishing off this game, and here's what happened and what I learned.
I chose to be Hatshepsut, which I am fairly certain was a wise choice. The creative trait is more than a little helpful on this map, given that the whole thing is giant border war. Also extremely helpful was the early War Chariot rush that allowed me to destroy Genghis Khan before HE could get the horses that were directly between his capital and my capital.
I started in the very nice Northeastern corner. GK was due west of me and then to his West (in the NW corner) was Sully. In the Southeast corner was Ragnar, whom I was able to ignore early because of the jungle separating us. Plus, he decided to declare war on his western neighbor Darius. Over in the Southwest corner was Lincoln, who took an early beating from centrally located Alexander, and has been low man on the charts the entire game.
What I learned is that with the good grassland start, and an early rush elimination of a neighbor, you can pretty much cottage yourself right to the head of the pack around the time of Liberalism. However, the wars were frequent so it was very important to actually pay attention to the religious situation and stay on the good side of the dangerous AI civs until you're ready for them. Even more so than on a Pangea map. I founded a religion and shrined it, but it was much more important to join the Hindu faith with Sully, Alexander and Ragnar. The first two could have crushed me, but I kept them on my good side.
Dopey Ragnar attacked me right as I was building up my army to be prepared for the Liberalism->Steel->everybody dies maneuver. I think I was 5 turns from Chemistry and then one more to complete Liberalism, so I just had to withstand a couple stacks of cats/swords/horsemen and then he was in trouble.
Oh, I forgot, he most likely declared war on me, because earlier I had jumped in to join his war with Darius. Poor Darius was doing pretty well with research, despite being constantly under attack from the Viking. He had settled a couple cities on my border, so I went ahead and captured them with trebs and maces, and then decided to go down and take one more (Confucian holy city) before accepting his capitulation. I then told Darius to stop researching Liberalism (which would have messed up my Steel plan) and set him on Divine Right. Sucker. Anyway, that left poor Ragnar all stuck in the corner with nobody to fight.
So, the game basically dictated that I shift into all out war mode right around when everybody was getting engineering and guilds. This is certainly different than a continents map. I'm not sure if it is even possible to go for a mostly peaceful game on this map.
It made me use a much less hybrid military/economy research strategy from what I normally like to use. It's been all about the military. I think the end game will be to add Lincoln to my stable of vassals (Darius, Ragnar, and Alexander), get them all up to speed with Rifles and then declare war on Sully. I still have a window where it will be cannons vs. muskets or lower.
Basically, this map would be an excellent way to get people to work on their war mongering skills. I'll probably end up suggesting it to people who ask how to improve in that area, since it sure seems unlikely that a person could avoid, or even delay, confrontation on a Great Plains map.