Yes, as far as I can tell puppet states count as non-occupied. I took it in my current game and checked unhappines before and after. So piety is great if you want to be a puppet making warmonger.
The bad thing about puppet states though is that they build stuff they'll never need such as unit XP buildings, which can waste a lot of gold.
Out of the first 3, I'd say it depends on your strategy. If you plan to have a small number of cities (for example if you're aiming for Gandhi's Bollywood achievement) and/or build lots of wonders go for Tradition. Aristocracy has good synergy with Egypt and Monarchy allows America to buy tiles at 25% of the normal cost. The bonuses for the capital city also work nicely for Rome (high population in capital = more production in capital = more buildings in capital = taking advantage of Augustus' special).
Liberty is best for big empires (founded, puppeted, or occupied). It works well for America (cheap settlers take advantage of superior scouting), France (early in the game +2 culture from an extra city will more than compensate the higher cost of social policies), and Rome (more cities that take advantage of Glory of Rome).
And Honor is obviously good for fighting. It has good synergy with Germany (easier to make that barbarian horde), China (double XP = double great generals for a civ that already gets more and better great generals), Songhai (easier to get the extra gold from pillaging encampments). And if I'm playing Greece I like to take it because then the game calls me Alexander the Great.
