What is your opener and why?

Emperor:
There's literally no rule. Sometimes I go monument first, sometimes 5 warriors, sometimes 3 scouts, sometimes scout and 3 settlers.

It depends on the map:
- more mountains, more settlers and warriors
- more jungle or forests - less workers; I sometimes go for 50 turns without building one
- more flat terrain more military units (barb scouts make it back to camp)
- too much good stuff in 2nd and 3rd ring means monument first
- more coast more slingers into archers (hello barb galleys, curse you)

Scouts are great if you play Germany or a few other civs, but should otherwise really start with a promo. As things are now, you're better off with warriors for most scenarios. And they should really buff spears vs barbs IMO, to give an incentive to build them. As things are now, I only build one if a city state quest asks.

In all cities I like to go monument or warriors first (or even chop in a city walls), depending on how aggressively I settled toward AI.

 

I can't speak for how wise this is, but nowadays I generally start with Slinger -> Warrior to explore and handle barb camps near me, and then the third depends on my Civ/Strategy. If I'm a seafaring civ (which I tend towards a lot) then I'll probably be done with sailing by then and pop out a galley for the era score and early shots at city states and then a worker to grab the sea resources and whatever else is around.

If I started near a wonder (I like "Legendary" starts and so it happens fairly often) I might rush Astrology first and plop down a Holy Site. (Importantly I've realized that one or two Holy Sites is enough, if they're well-placed and my other religion choices are well-chosen.) Otherwise probably another Warrior.

I've found that I'll likely get an early scout and/or builder from Goody Huts, so I don't emphasize them in the first 20 turns unless I have to.

 

Emperor Difficulty
Scout - Warrior - Settler

Scout for finding huts, city spots, city states, barb camps, etc. Scout first is probably the best option on anything but Deity
Warrior for barb camps/escorting settler
I usually try to buy a builder, 200 gold doesn't take very long to obtain. The builder is for the 3 improved tiles inspiration and to improve the luxury for amenities. I also don't chop often and I pump out settlers from my capital losing population to work improved tiles until Magnus