For the "beginner" pantheon, I'd definitely suggest going with the Greek for that.
That's basically what I'm leaning towards now. I've got some complex metrics by which I balance the pantheons, and everything I've got has told me the Greeks are going to be the easy choice. (Not the BEST choice, but the least likely to cripple you if you don't know what you're doing since they focus the most on the simpler choices.) The main reason I hadn't put them at the 2/2/2 slot initially was the AoM game itself, where the Greeks got their Favor from priests; since they were the cause of one of the three methods I'm using, it felt wrong to take that from them. But I don't worry about that too much.
while you don't exactly see temples in Native American tribes (if you do go for a Native American pantheon--which I think would be a lot of fun, having researched some of their mythology myself--I'd suggest the pluses to x3 Priest and x2 Combat favor).
This is one of the reasons I put the Aztec as Battle/Buildings; they DID have temples. Right now the Priest/Battle combo is the Sumerians, but if the Greek Priest/Building slot is freed up by moving them to the 2/2/2 combo, then Priest/Building is good for the Sumerians. Now, the Hindu one at Buildings/Priests is kind of strange, so I might give that one to the Sumerians instead and shift Hindu to Priest/Building. That'd keep Priest/Battle free for the seventh set I'll add.
That being said, there may be a way around it that combines the two. Each primary god might unlock different myth units to build at different techs (rather than through the shrines/churches/cathedrals/basilica, or through favor), and some gods might share certain units that make sense (particularly within a pantheon).
That's not bad, but let me explain what I've got right now. Currently, all myth units unlock with specific levels of religious buildng, but the caps for building level depend on tech. There are four levels of building: Shrine, Church, Cathedral, Basilica. But ignore the names, and go L1 to L4.
When you take the first religious tech (Mysticism), you unlock L1 in you main god's primary focus. All cities immediately get a Shrine for that focus, but it can't improve yet. Since very few foci add a unit at level 1 (I think only Animals does, currently), it doesn't really enter into this discussion.
The second religious tech (Deism) unlocks L2 in the primary and L1 in the secondary. Your Shrines don't immediately grow to L2; you have to upgrade them through generating Favor.
The third tier (late Ancient Era) has two religious techs branching off Deism: Polytheism (unlocks level 1 buildings for minor gods) and Hierarchy (allows your capital to be one level higher than the cap).
There are more techs, but that last bit is important to this discussion: since the normal unlocks cap at L3 for primary/secondary and L2 for minor gods, you'll only EVER be able to reach level 4 in your capital, and only for your main god (both his primary and secondary). Even the minor gods will only hit L3 in your capital, and only in a very narrow tech window (since Monotheism LOWERS the minor god cap). So, any units placed at L4 within a focus will be, by the nature of the system, exclusive to those gods that have that Focus, and the Primary focus will hit L4 two tech tiers before the secondary does. (In fact, it's likely you'll have the Enlightenment before you ever see your secondary hit L4, so I'm not worrying about that.) L3s will be almost as restricted, in practice.
For 13 of the 21 foci, only one single pantheon has a god with that focus as his/her primary (and no Focus has more than three pantheons with it as a primary). Loki is the only fire-primary, Inanna is the only beauty-primary, Isis is the only fertility-primary, Ra is the only animals-primary, and so on. So, if I make that L4 unit be something specific to the appropriate pantheon, then it's very unlikely that you'd ever encounter it outside of someone who went with that pantheon; no need to make pantheon-specific alternatives. For instance, Poseidon is the only major god to have a Water primary, so if the L4 Water ability is to unlock Scylla, only Poseidon devotees will generally be able to build that particular creature.
Another point: I take issue with Loki's foci! Fire/Crafts would put him in Lawful to begin with, and to me that just doesn't seem right.
Loki was a tough fit, no question. But actually, Fire is CE (which as the primary would be -2,-2) and Crafts is L (which as a secondary is +2,0), so he'd start off at (0,-2). Balanced on the law-chaos axis, negative on the material-ephemeral. I'd also been looking at having Favor generation methods shift by +1 or +2, but that was back when I had four methods instead of three. (The method I dropped involved creating Missionary units, but AI limitations killed that one.) Battle-generated favor, obviously, was originally the one on the C direction, which would have deliberately skewed the Norse and Aztecs in that direction a bit.
Admittedly, I don't fully understand your criteria about balancing different pantheons with regard to what foci are excluded, but switching out Crafts for Darkness (assuming Darkness is Chaotic) on Loki would make more sense to me.
Darkness is Ephemeral; the Chaotic focus in the fifth set is Storms, which Thor has as his secondary (partially canceling his LE Air primary). So switching Loki to Fire/Darkness would put him at (-2,-4), somewhat chaotic and VERY far down on the E axis. While that'd give him early access to the Art and Beauty domains (great for culture and happiness), it'd make a pretty large number of foci unreachable. One reason I like that change, though, is that in my old setup I'd put both Thor and Loki at (0,-2) to start; they'd play too much the same, then.
As to which is more appropriate, thematically? Crafts is basically +Production (it's Hephaestus' specialty), while Darkness is the Hunter-Seeker Algorithm. That's the National Wonder in my SMAC mod that reduces enemy units' visibility and range once they enter your territory; I want that to be the L2 Darkness effect, with the L4 being basically -3 visibility. Units would never be able to see anything but the cities (at least, once they enter your lands; from outside they could see in) and would attack blindly, which'd be a HUGE boost to your defensive ability. Now that does sound pretty Loki-ish, so I'll probably shift it; I set up his foci back before I added that particular focus to the game. I want to check my grids at home before deciding on this, though.
And what I meant about balancing is this: let's take Loki as I had him before. He wouldn't be able to pick Travel, Storms, or Balance, because those are the secondaries of the other Norse major deities (if you add a major deity as a minor you only get his primary). He also wouldn't be able to pick Healing, Plants, Seasons, or Darkness because no one in the Norse pantheon has those. Every god has a different set of seven off-limits foci like this. Now, that particular group of seven consists of two Ms, one L, one E, two Cs, and Balance is the neutral focus (0,0); add those to the CE and L he starts with (and therefore can't add again), and you're still very balanced in your remaining 12 choices. So it's a very safe mix; no one part of the mandala becomes inhospitable to him, where an AI could quickly get stranded with no choices. (I've got a script that plots out numbers for this. It's messy.) If I were to switch his secondary to Darkness and not change anyone else to pick up Crafts, then his banned seven would include 2 Ms, 2 Ls, 2 Cs, no Es, and Balance, but the 12 available foci would stay the same as before so it's still safe as long as I don't decide to switch anyone else around.
Now if I had it giving, say, 3 Ms and 3 Ls, then that'd be a serious problem because it'd basically force anyone who picked Loki to play in one small area of the grid, which means you'd end up with the same minor gods every time you played. I wanted to avoid that if possible.