N3O Age Of Empires and Starcraft 2 Clan

I've never played played a team game yet, but I am hoping to get in on some N3O team action tonight. So, I've never really bothered grabbing any of the team cards for my civilization, which is Spain. (Side note: I don't have a lot of time to play online, so I'm focusing on getting Spain up to level 40 or 50 before playing other civs, so I will be able to start new civs at a decent level)
Anyways, I've got a few cards available right now, and I was going to ask which Spanish TEAM cards I should definitely pick up. (My city is ~22) The card that stands out to me as being Spain's best team card is Inquisition. After that, most the other cards seem to be more strategy-specific.

I was trying to figure out in what situations you would play the Archaic Soldier Training over the Cheap Barracks. Cheap Barracks gives you two barracks for the price of one, which effectively halves the train time ALL infantry in groups of ten, right? I guess the only exception would be if you want to train five or less, but if were going to train five or less, why play AST at all? Or maybe there is some crazy Spain + Britain ambush strategy involving AST and Fenching school (-90% train time, right?) where you bait the enemy into Britain's base and then spring an instant army of longbows on them?

Any great Spanish TEAM cards I'm missing?

archaic training is 100x better than the cheap rax card.
It's one of the few good spanish team cards, inquisition is ok-ish

Do you mind explaining why archaic training is considered so much better? I'm a fairly new player so I'm just thinking of it from a numbers perspective. Maybe there is some key strategy issues that I am missing. Perhaps I'm underestimating how critical waiting an extra 13.5 seconds for your first wave of defense can be when your TC is under attack in colonial?

With archaic training, you build one barracks for 200W, and can produce 5 xbows/pikes every 27/2=13.5 seconds, or 10 in 27 seconds. With cheap barracks, you build two barracks for 200W, and can produce 10 xbows/pikes in 27 seconds. The numbers scale identically with more barracks, as well. (3 barracks for 600W produces 30 in 27 seconds, or 6 barracks for 600W produces 30 in 27 seconds)

Archaic Training Pros:
Five units come in 13.5 seconds.
Archaic Training Cons:
Only certain units train faster.
Fewer barracks can be destroyed quicker.

Cheap Barracks Pros:
ALL infantry train twice as fast using this method, but only in batches of 10.
Extra XP from building additional barracks. Or does the XP go down with building cost??
Two barracks take twice as long for your opponent to bring down.
Cheap Barracks Cons:
You lose 30VS to build the second barracks, so really the cost is +15-20W per additional barracks depending on your gather rates.
Five units still take 27 seconds to train.

2 rax doesn't make training units any faster, plus, even with the archaic training, you will often spam from 2 raxes, so you would need to build 4 raxes to get the same nr of units out.
the first batch is also already fighting before the 10 will.
If you got 1 rax at your base, its easy to spam some pikes in case of a raid. Speed does matter.
After you sent fencing school and do the church tech: standing army, pikes and xbows are instand speed

Archaic training is an amazing card. The only other two team cards I would ever consider playing are team LOS increased +10 range and team hand infantry attacked +15%.

All the others are pretty much junk -- team 1 monitor, team explorer, and team cheap priests (or whatever). I know some will disagree with the last one, but I have yet to see it actually effectively be executed in the russia/spain missionary sling.

I've seen it and it's quite OP if well executed.