Now let's see:
1. Archery unlocks Archer, Skirmisher, Bowman, Longbowman, Crossbowman, Cho-Ko-Nu, Horse Archer, Numidian Cavalry, Keshik, Camel Archer ie 10 units.
Rifling unlocks Rifleman, Redcoat, Infantry, Marine, Navy SEAL, Paratrooper, Tank, Panzer, Mechanized Infantry, Cavalry, Cossack ie 11 units.
Horseback Riding unlocks Horse Archer, Numidian Cav., Keshik, Knight, Camel Archer, Cataphract, Conquistador, Cuirassier, Cavalry, Cossack, War Elephant, Ballista Elephant ie 12 units.
So,
Horseback riding unlocks the maximum number of units in the game. Although, you can see that for any particular civ that you are playing, Rifling will win hands down. That's why I specifically said to include all civs.
2. Corporation unlocks all 7 corporation buildings + Wall Street ie 8 buildings.
Masonry unlocks Walls, Dun, Aqueduct, Hammam, Baray, Pyramids, Great Lighthouse, Great Wall ie 8 buildings.
Meditation unlocks all 7 monasteries.
Music unlocks all 7 cathedrals + Sistine Chapel ie 8 buildings.
Priesthood unlocks all 7 temples + Oracle PLUS the clincher ie the Ziggurat, which makes it 9 buildings for it. So,
Priesthood is the correct answer!
Note that Meditation and Priesthood also unlock Buddhism's and Hinduism's holy shrines respectively, but that would still make Priesthood as the winner.
So you are right Bob the Barbari. Ask away
