Overall, I think that later civics should tend to be more valuable than earlier ones. Otherwise, why bother with trying to research the required techs? Whether "better" is because they are just plain better or because they tend to be more useful based on later stages of the game doesn't matter. It's okay to go for different strategies and such but if the mroe advanced civics are niche tools with respect to strategy they should be pretty darn effective in that niche.
On food: Food drives the game. Anything manipulating food production is going to be very twitchy to balance. Balancing it is going to be like making fine adjustments with a 5 pound sledgehammer.
GOVERNMENT
Despotism - Abandon ASAP. That's okay, since it's where you start. I might witch back if I were desperate due to war weariness, but it would have to be horrendously bad.
City States - This is the bulk of the game for me.
God King - Early game. Get there quickly and stay there up until 4-7 cities, depending on how close they can be to the capital. Switch to City States when the maintenance gets too high.
Aristocracy - Bordering useless in all but one situation - Agriculture civic and Financial civ. Aside from that, I'll take the extra food and run specialists for equal commerce yield plus GPP. A couple of settled GPs will easily outstrip the benefits from this. Only with financial to add to the commerce yield is this worth it.
Theocracy - Could be good, but since I tend to end up with a large, hard-to-maintain empire, the bonuses usually aren't worth moving out of City States.
Republic - Only if happiness gets out of hand.
CULTURAL VALUES
General commentary: The initial options are all useful at different points in the early game but not so much that it's worth changing to. Well balanced overall, imho. Unless Spiritual, I just stick with whatever the default is in most cases. As a spiritual civ, though, the order seems like a no-brainer: 1) switch to nationhood to get those early warriors out, 2) switch to pacifism once you can assign specialists to get some bonus GP while troop levels are low, 3) switch to religion as religions come on line because by that time your cities are big enough to need the help.
Religion - Obvious use. Decent option for a religion-oriented strategy.civ.
Pacifism - Good in early game, but quickly becomes virtually impossible to maintain in the later game. Once the AC gets up there, you will be in war and not having troops is suicide.
Nationhood - Good in early game for defense.
Social Order - I've only used this a couple times and noticed no great benefit.
Consumption - Good for balancing an overextended empire (which I am wont to do), but not so great as to want to stay there if the economy can be balanced other wasy. A good balanced option, imho.
Liberty - Specialists are always fabulous. A good late-game option if the economy allows.
Crusade - Can't see this as anything but a desperation ploy.
LABOR
Slavery: Whipping-based strats are legion in vanilla and many of them port over to FFH. Since this takes a lot of effort to get to and requires giving up gold rushing, it's definitly not too powerful. It may be a little bit weak simply by comparison. The only time I actually use this is if I end up in a position to grab OO.
Arete: A solid civic. The mine bonus can make for a monster production city. The only downside is that it comes from a dead end tech aside from this decent civic.
Military State: Good for gearing up for war or defending on short notice. I will park here with a decent economy but otherwise it's not terribly attractive. Application is limited to the point I wouldn't bother researching the tech needed.
Serfdom: I just don't use this, but I have no reason why...
Caste System: Obviously very good for a Specialist Economy. A solid choice.
Guilds: Theoretically, unlimited merchants could be amazing. Unlimited Merchants, with Agriculture and a high happiness cap means one city can virtually support an empire. This strategy was set up for vanilla (Caste System and Globe Theater) not too long after the initial release. Each Great Merchant provides more food, allowing the specialist count to rise, creating more GPP, etc.. In practice, this comes at such a late time that it's impractical and the other bonuses aren't that great. Overall, it's of very limited use.
ECONOMY
Decentralization - Fine as a starter
Agriculture - Good for early growth and getting a SE running. Good for a production center or civs stuck in borderline terrain (Tundra and such). Also good in combination with any of the whipping strategies. Extremely versatile for such an early/cheap civic. Switch ASAP and this is the default.
Conquest - Almost never use this. I'll take the extra food and work mines or run priests or engineers for more production. It can help squeeze out more military production in a hill-poor area, but it's a very minor niche. Unless the game situation just happens to fit that niche, the bonus XP isn't worth it.
Mercantile - Like Consumption, a nice option for balancing an over-extended economy. Still, it's usually back to Ag if feasible.
Foreign Trade - Mathematically, this never adds up in the game. Unless you are running a very low gold slider, the trade routes don't come close to making up for the loss. It's really only useful if you need a culture boost.
Guardian of Nature - Good for FoL, elvish civs (or those that captured lots of Elven Workers). Otherwise, just not worth it.
COMPASSION
Sacrifice the Weak - Good for whipping strats, especially since it can be combined with gold rush civs. Limitation based on alignment makes up for that. Overall, balanced.
Fend for Themselves - I don't see the point of this. Civ maintenance is so small a part of economic cost that this just isn't worth it. Definitely needs a boost of some sort.
Basic Care - I stay in this most of the game, unless Expansive.
Protect the Meek - The lower cost for Expansive civs means this is a free benefit, so it's definitely worth a turn of anarchy to switch.
Public Healers - I'm not doing this unless I have a desperate need for health and/or happiness.
EDUCATION
No School System - Starter civic. No problem.
Apprenticeship - A good bonus/penalty mix for the point at which you get it but with an offsetting production bonus for Nationhood, there's no reason not to go here immediately. A good spot to park until better Religious Discipline or Scholarship open up.
Military Discipline - Good for during a war when you need both quick production and reduced weariness. Otherwise, stay away. Very situational but useful.
Religious Discipline - Great if you want to run a priest economy and/or go for an Altar win. Research bonus is good otherwise.
Scholarship - Great for running SE, unless you need to fight. Good balance choice against Religious Discipline.
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Edit: Somehow I missed the fact that Aristocracy is +2 commerce for -1 food. That makes the commerce tradeoff much better in comparison to specialists. I think it should work well for Financial civs that automatically get their bonus on all tiles. For a normal civ I would still probably still choose priest or engineer specialists in most cases. My estimate on the value hammers is close to 2 commerce, and the GPP tip the scales for non-financial civs. Obviously, I haven't played it since I didn't realize it was +2 commerce. This is all theory at this point, but without trying it I'd call Aristocarcy sitautionally useful.