Here's my stab at it. I'm thinking the founding city (1) would make a good production center: plenty of food, and I'd be surprised if iron or horses didn't pop up somewhere else in it's bfc (two resources seems pretty weak for a typical founding site). Of course, it might just be uranium and aluminum though.
2 second for reasons already mentioned (too much chopping for 3). It also has a strong production base and food base for the early game, which should really help whip out those early rushers. Later, I'd leave it for a decent science/commerce (s/c from now on) city. Not great, but you could always switch to some limited production role if the situation called for it (plains, plains hill, and copper guarantee it would be useful), and otherwise just work the cottages until late game when it grew to 14+ pop.
3 and 4 might actually be better after 5, now that I consider the jungle limitations. I think 3 would be your best bet for a GP farm: pigs and 3 flood plains, plus an easily irrigated grasslands should be enough. Of course, shift 7 down one and it could work well, too. I'm not huge on GP farms, so perhaps it's a little weak.
3 could be a real production city. Grasslands all around, plus food extra on some, plenty of hills, and corn to boot! Correct me if I'm wrong, but the sugar should still produce 3 food even if it isn't being plantationed, which means workshop spam, mine the hills, and there you go. Perhaps some plains hills and metal/stone resources would be nice, but you might just get lucky yet...
4, general commerce. The fact is that there's probably something lurking in there, like iron or oil, as that's a lot of ground for just one resource.
6, general commerce. Same for 7 and 8. Gotta love financial leaders, as coastal cities can still work out well.
9 is sort of a "whatever" city, although if you're going for a wonder that gets discounted with stone, you might want to take it early.
Really, without seeing what's below and above it's hard to tell exactly what to do with the other squares, and the exact order. You might find that Caesar has much nicer land... He should really share it. In fact, I think it's your duty to make sure he does share it with everyone... but you should also take a cut for letting everyone share it, say around a 100% cut. Same with Genghis.
Kidding aside, this is a pretty good start. I'd prefer to have both civs on the same side in case of a double-team. Keep an eye on your back. I'd prefer to attack Khan first, simply because that's the direction we're thinking of expanding into, and you can quickly cut Caesar off with 2. Then again, Khan might be too far for an effective rush. In fact, it'd be 16-17 turns before your first axes showed up... bleh. He'd be too well fortified by then probably.