I did my Civ 4 and 5 around King and Emperor. If we do get a WarRoom game going I'd probably just bump it down another touch to Warlord so that someone doesn't get wiped before even meeting the other Sherbros. I got invaded by 14 warriors by China once and couldn't hold them back as I didn't have any iron for swordsmen that playthrough (Prince). My Civ 4 and 5 strategy was always don't give a rip about military until swordsmen or even knights but that no longer flies at all.
Aggressive barbarians. If a scout sees your city, he'll return to his base and show up ~5 turns later with 3 spearmen and an archer at a time where you still only have warriors and a slinger if you didn't go up the military early research path. Tip 1 I'd give is to build scouts early to chase them away from your perimeter and never let barbarian scouts see your cities.
The city districts are a wonderful addition. Really benefits your cities to make each a specialist rather than balanced. Workers and roads have changes up a lot too that I didn't like at first, but realize is needed to prevent the army of workers you have late game you never really needed to acquire since ancient days. Certain tasks can cut research in half for different discoveries (like killing 3 enemies with a slinger gives you 50% archery tech, discovering another Civ gives you 50% writing) and I like that as even historically so many techs were discovered as "eureka!" moments rather than simply pouring money and time into them. I bet there's a guide somewhere for best way to chain all these tech boosts together, but I find it more fun to figure out for myself
Its also not as crystal clear to me (yet at least) where the prime spots to build a city are. Something may look good to me at first, and then in medieval ages I'll realize my #2 city sucks and now I can't just focus on Wonders out of my capitol like I like to do.