
Alright, I've taken a second look, and some things come to mind.
First of all, you may be on the defensive for a while. Axemen aren't going to do much to Sitting Bull's Archers, especially if he has Totem Poles, which he should. Same with the Dog Soldiers, which he'll probably build a lot of, because he's got no iron/bronze in his two current cities. The good news is that Sitting Bull's Archers are defensive, and his Dog Soldiers are weak against Archers, so he's not going to come after you before either of you get Catapults.
Montezuma is another story. His Archers don't get any bonuses beyond Barracks, and his Jaguars aren't that great. He also doesn't have iron/bronze in his two current cities, so depending on where he places his third, he may be an easier target. If you don't settle Mississippi, he may even go for it instead of a copper city (though I'm not sure the AI is
that stupid). Since he's a madman though, I'd still wait for Catapults.
Speaking of Catapults - have I mentioned them yet?

- that's probably the Captain Obvious tech to beeline after Archery & Mysticism. Enough suicide Catapults will take down any city, and any SoD Monty would want to send your way (instead of Pacal's or Sitting Bull's) will find it an uphill struggle after getting hit by the same. Plus, Masonry is on the path to Construction, so that's a bonus.
The only two real questions regarding the tech path are whether to go
Animal Husbandry -> Writing or
Wheel -> Pottery -> Writing, and if you want to grab Iron Working before grabbing Construction. Animal Husbandry is surprisingly worthless in North America with no Horses, Cows, Sheep, or Pigs... but it is cheaper than Wheel & Pottery. Still, you're going to need the Wheel no matter what, so that's probably the better path.
As for Iron Working, I honestly don't know. It would boost production in the capital and give you another resource for spawning units, but Swordsmen aren't going to do much better against Sitting Bull's defensive bonanza than Axemen. They may help if you decide to target Monty, but only marginally better than CR Axemen. Perhaps the first tech to target after Construction?
Now, for where to place your Settler, here's what I'm thinking (dotmap):
Mississippi's only value to you would be to block and/or have a cottage city. Both don't really help you right now, especially with how bad it's production will be before the late game. Jacksonville is even more of a waste of your resources & time.
You will get some pretty good production out of Toronto & New England, especially with an army of workers laying down farms, mines, and chopping out buddies. Toronto would be my first move, to block out SB and get the fur bonus, then Portland with the third Settler. Portland will be an especially good military city.
You could settle Toronto 1N on the Uranium. That would give New York two extra tiles to work with, as well as allow Toronto to build a Lighthouse to make those Lake Huron & Lake Eerie tiles super productive, but it'd also give you three more worthless tundra. Settling on the Uranium I feel is more powerful long term, and right now you want short term.
Oh, and New York obviously won't do much for you past a pop of 9, but it gets crab, would be a good Moai Statue location, and all those 6 coastal tiles won't exactly hurt your tech rate. Backfill location, naturally, but a decent one.
Game's not over yet.
EDIT: D'oh! Portland would probably do even better 1N of the Fish instead of 1NW. That would free up 3 tiles for Toronto, another for New York, and give you an extra hill to work with. Can't believe I didn't see that before. Oh, well. I'm in no mood to redraw the whole dotmap. My mistake. Also set behind a spoiler because I don't want to distract from Neal's posts with my own pics.