Hordes aren't my cup of tea, but with the Aztecs you either win the initial battle for the seas and trash their main fleet, or you die. Any fleet with more than 2-3 transports needs to die, and die now.
This is the preferred method. It is technically possible to quickly Christianize and ally France or some such if you're lucky enough not to be attacked before switching, but that's a hell of an opening to leave open to chance in such a way especially when you don't have to do so.
As for hordes:
-was administration the best first pick?
I'm not sure. Reforming early is bad, but ADM first might not be. The reason that reforming early sucks for Mongolia is that until horde units fall off really hard around MIL 12, 4 pip infantry and 6 pip cavalry are going to be reasonably competitive, especially the cavalry. Mongolia reforms into Chinese tech unless you switch to Sunni (which is annoying to do as you have to dump Buddhist majority land), so there's no much rush as Chinese is 15% better but gets worse rulers. Horde LA sucks but your land isn't good anyway, so you're going to piggyback off looting Ming and trade for some time. Also, tribal conquest allows for 0 DIP vassal feeding without religious.
There is an idea group crunch here. Intolerance is very painful if you conquer a lot of off-religion you can't convert, so you want humanist or religious. But, you need another admin group to reform, and opening 2 admin groups is going to be draining. Alternative, you can forgo it all and grab aristocratic (more early cavalry power) or diplomatic (more vassal feeding per Ming war).
Mongolia does not have any special tolerance of heathens. As a result, humanist only gets you to +1 to +2 range (depending on legitimacy) if Buddhist. That's okay, but not worth an early investment you don't need. You need money too though and ADM doesn't get you that. I might actually suggest economic or innovative here. That crap clan council to the north has gold, so economic will help a bit with the inflation but also with manufactories. Innovative makes advisor costs less bad and also dovetails well with farming up army tradition, something you'll be doing often.
I haven't experimented with Mongolia TOO much in 1.8, mind you, but maybe this patch I'd open innovative or administrative (you don't pay to reinforce mercs more than the usual maintenance, so there's some benefit to this aspect of administrative too), full annex --> release the Sunni hordes into Buddhist (they'll take enforce heritage and some take religious first to ease some of your tolerance problems), force religion on your vassals to the East as you take them, and try to break Muscovy while still a horde. Nailing them while they're reeling from league wars or Commonwealth is probably a good time. Once you border LO or Sweden, reform the government and westernize. Alternatively, if it's taking too long just reform the government. Focus military so you can keep up in troop quality.
When vassal feeding Ming, you want to either make sure your vassals are Buddhist and stay that way, or that you go Confucian. You're not taking influence early here, so the extra +1 from religion is very helpful for annexing a big vassal. Make sure you loot Ming like crazy since the money really helps tough wars.
1.8 has some cheezy peezy potential that I haven't experimented with yet from Monglia's position, like tearing a vassal out of QQ or some such to get near Ottomans using support rebel CB, rival Muscovy and use that to get friendly status w/ Ottomans and bring them in on Muscovy. Persia's a good bet if it's after the time period they can convert to Shia, since they'll convert land for you and can be fed land you need later, and will let you core an adjacent province in Asia to eliminate the distance ally penalty. A similar technique might be useful to bring in Commonwealth on Muscovy, using one of the "Asian" guys near Georgia.
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