I've been experimenting as Monty lately - though nowhere near Immortal level - and I can say his UB is fabulous when the circumstances are right.
At the risk of stating the obvious, here's what seems to work best for him:
Key techs: Farming/AH/Fishing (depending on available resources), Pottery (but NOT for cottages, only for the graneries!), IW and CoL. You'll obviously want to pick up Writing (for specialists) and BW (for Slavery) along the way, but being on the paths to aforementioned techs that's a given anyhow.
I wouldn't bother with early religions or wonders either. Only exception: if you can pull off an Oracle slingshot to CoL do so, but I wouldn't jump through hoops to get there either.
Strategy: forget cottages and mines alltogether, just farm farm farm. Go after food-rich locations first: 2 food resources or a few FP's are a minimum.
Also try to locate horses ASAP and settle near them if you can. Why horses? You'll want to rely on your UU and the best counter against the Jaguar are axemen. Hence, chariots help protect your stacks. Moroever, they make great medic units, excellent barb protection and good scout replacements once the barbs start popping up. Other strategic resources are far less important though, with the possible exception of marble for Oracle.
Get a granary, barracks and library up in your early cities soon. Then play the swapping game: alternate between growth, specialists (primarily GS) and whipping. Amass Jaguars - with an occasional chariot and perhaps a spear thrown in for good measure - along the way.
Expand through war once you're strong enough to pick on your neighbours. Play the Monty we all know and hate (or love): kill, raze, pillage and esp. be utterly relentless. The window of opportunity of the Jaguar is fairly small so you really need to push hard to make the most of them.
If possible, build (or rather, whip) a sacrificial altar FIRST in newly conquered cities, then barracks and granary (the sequence's less important there). Use those cities as advanced troop-generating hubs: they'll most likely won't produce anything worthwhile for a bit in the way of commerce/beakers anyhow. Rely on your core cities & specialists for research instead. With the altars in place maintenance shouldn't be much of an issue as well. Above all, the nifty little things allow for virtually incessant whipping!
After CoL/IW I'd recommend Construction (= catapults) and civic-enabling techs. The latter are mainly useful to optimise the grow/whip/specialist cycle.