Which leader you using? They each have their own unique start biases. If you're using Russia you're gonna start on Tundra often for example. Desert with Mansa Musa, ect
Archery helps a lot. I'll beeline it if I'm having barb issues. If you have two slingers you can upgrade them for 120g and that'll hold off most any barb threat until you can build up enough melee units to kill the camp
My favorite way to play Civ is to remove barbs, play a Pangea/single land mass game, and then max the total allowable civs on a tiny or small map in advanced settings and just have constant war.
The main thing for me is just remembering to think about how a certain governor I have could be advantageous elsewhere. Like if I start a new city that can do a lot of chopping I'll forget to move Magnus there. Or sometimes it's efficient to move Reyna somewhere quick to buy a district or two before moving her back to a Market+Harbour city.
Haven't played previous Civs so not sure of the mechanic was similar, but try keep up with checking what tiles your people are working. The automatic assign is pretty good but sometimes you'll want to do something different, especially if you're trying to grow with food and stuff
Big Civ V “population management” guy. Lots more nuance in this version. v cool a volcano just killed my warriors but the food output doubled. Gaia provides
Civ 6 does have some very manually intensive worker management mechanics but you can ignore it and get 80% of the efficiency.