I usually play Emperor. Scout first unless either very high production or low production initial tiles (in which case builder first to capitalise on high production tiles or boost low production city).
After that, at least one or two settlers, one builder, at least one more melee. Go from there. Not sure where is best to spend my early gold. I used to buy a builder, but now I usually build it. Another settler or a monument seem like the best options.
I try to avoid early slingers / archers. I’ll go for the archery boost early if I have horses and a horseman rush is viable. Archers are great defensively early game but I’m not sure they are really that strong on offence - I’m still experimenting, but certainly just a couple of melee plus my scout seem to work better. I feel always building early archers can become a crutch. You have to build them eventually though for the eurekas.
Is scout the most efficient opening? Don’t know, really. But it’s certainly the most fun. I think exploring the map has advantages, but in any event the game is more fun if you do. And after a few settlers and a builder, and one more warrior, my levelled up scout and two warriors are pretty formidable until I build some reinforcements. And diplomacy is a good defence too, as is initiating DoWs if you have the terrain. Later on I explore with religious units, maybe a great person (although that feels like cheating), maybe a caravel.
If you want let’s plays, theGameMechanic on twitch is great. He plays fairly well. Very early game is strong - good city placement and prioritisation, and effective use of chops. After that, he builds way too many districts, way too many IZ (as in ‘more than one, and like maybe you shouldn’t build any’), avoids coastal cities too much, and he’s not very efficient getting religion. But good chat, and some insightful comments. Note his Twitch is much better than his youtube.
[edit: poor expression in my first para.]