Okay, I finally had time to think properly about this. So lets see which civs suit our Agri/Fish/Mining requirement:
America - Agri/Fish, Musket with G1, W1, Barracks that gives Melee 5xp, mounted and gunpowder 4xp.
This would suit a CHA leader, but does sound pretty good on a land map.
Carthage - Agri/Mine, HA with +35% vs non-spear melee, Harbour with extra trade route
Great techs, average everything else.
China - Agri/Mine, Crossbow which doesn't do much more than a regular crossbow any more, Theatre at Aesthetics.
Great techs, rubbish everything else.
Dutch - Agri/Fish, Strength 6 galleon, Customs house with gold for rivers.
Classic water map very late civ. Not much of interest.
England - Agri/Mine, Amphibious Rifle that gets +25% vs gunpowder, bank with +15% beakers.
Pretty nice, but too late.
Korea - Agri/Mine, cat with +50% vs melee, uni with +15% beakers.
The cat vs melee thing doesn't impress me because your neighbours will build archers or horse archers, the uni is the definition of dull and late. Sorry I'm not a big fan!
Portugal - Mine/Fish, Caravel with +1 cargo space, customs house with gold for water tiles.
Watery. No thanks!
Rome - amazing but taken
I don't like any of those.

If we expand our net to include civs with just one of our required techs then my thoughts are:
Arabia - Agri/myst, knight that heals on the move, library with priest slot.
Great for a religion, great for attacking at knights.
Babylon - Agri/wheel, Archer that gets +50% vs melee, 45h granary that you don't need pottery for.
I can't decide if the early granary is a trap - stopping you building settlers when they're a better return than the granary anyway.
Byz - no cataphract
Egypt - we're not attacking anyone with chariots are we? Please?
Ethiopia - Sentry is a good promo, but otherwise a bit boring.
France - Agri/wheel, 2-move musket, observatory with extra specialists.
Worth it for draftable 2-movers...
Germany - hunt/mine, str14 grenadier, forge with -25% maint.
Should expand faster for longer. I don't value Mil Sci so much on a pangea - it's a water map tech for me...
Greece - meh
Inca - Agri/myst, warrior that you can build until Civil Service, 45 hammer granary that gives culture.
Amazing. Must have. Why is this granary 45 hammers?
India - taken
Japan - drill 2 is overrated.
Khmer - the elephant that takes down a knight is okay on the defensive, but we want something that helps us attack.
Mali - agri/wheel, str 4 archer, forge with +10% gold and beakers.
Should help expansion phase, but doesn't bring me joy.
Maya - str 5 spear is nice, but otherwise boring.
Native America - agri/hunt, scout that can build totem pole and heal units +15%, monument that gives archery and gunpowder units xp.
I'm pretty excited about the insta-build 15 hammer monument, especially with the changes to barbs that mean you want to build scouts at the start of the game instead of warriors. I haven't been able to convince anyone else that this is exciting yet.
Ottoman - draftable musket that gets +25% vs older units sounds good.
Persia - Immortals are rubbish now.
Russia - Cav that kills cav! A bit late.
Spain - meh
Sumeria - agri/wheel, str6 axe which loses 25% vs melee, 90h Courthouse at writing.
The axe is pretty handy vs mounted and archers, and the cheap courthouse is nice, but probably not needed so early.
Zulu - agri/hunt, 2-move spear with -40% vs archers, barracks with -20% maint.
If you want to run over someone with horse archers this is your stack defender. If you want to get embroiled in an ancient era war that benefits neither of you the Impi is your man!
My favourite is Inca paired with IMP and something economic, followed by Arabia if the plan is to attack at guilds and try for a (later?) religion, Zulu if the plan is to attack at HBR. Sumeria and Natives are both decent enough, I guess Babylon is too, but I think the flexibility means that I'd choose Inca (again - see pb46 for how good it is). The hammers saved on granary and monument and the beakers saved on religion can expand us fast which helps to get to economic techs fast (alphabet isn't so hot on a pangea, where open borders won't beat ICTRs from an island, but currency should still be the king).