A couple of tips to help out those who seem to be having trouble with GOTM1, based on my experience:
1. There's not nearly enough space to grow and win this one peacefully in any reasonable length of time. Get stuck in early and often, and use your immortals like the disposable shock troops that they are. Otherwise you'll still be stuck negotiating with the aztecs for resources in the 20th century.
2. The aztecs will give you all kinds of grief with those damned 2-move jag warriors. I was successful in containing him, after losing a stray warrior in the open, by putting a spearman next to his capital, fortified atop a hill. This kept him agitated enough that I was able to expand twice and get iron, buying me time to kick his butt with the immortals.
3. Bust out da whip. Early, often, and especially in just-captured cities where them defecting may be an issue.
4. When attacking with immortals, try to do it in waves instead of singly, and keep back 1 or two healthy ones to protect the victorious ones that have lost health. I never wound up getting a leader because the AI kept swooping in and assassinating wounded elite units that I left exposed.
That is all I have for now.
Cheers,
Callahan