So we all know what to build first, we got 2 pages in this 1 thread alone, but my next problems are emerging.
What should i focus on w/ that worker? production, growth, etc.
I notice that if i focus on growth my city gets too crowded, and i'm not sure how to fix it. I know starving the city works, but there has to be another way.
There is! It's called "beating your people to death until they make nice stuff for you"! It's great!
But how you use your worker(s) depends a lot on where you start, what worker techs you've got researched, etc etc. In the very start, maximising food and production is your friend (your palace gives you so much commerce that focusing on maximising commerce right at the very start is - gold or gem mine excepted - rarely a worthwhile move). You probably want one high-food square that will grow you to size 2 ASAP (so you probably want to prioritise researching the tech that lets you exploit any food special you have - although husbandry can maybe wait a bit), and then really, you're best off improving those squares that will give you the max food/production total. Food gives you more people who can switch to high-production squares, or who can just be whipped to build stuff, so increasing food crudely equates to increasing production. For building settlers and workers, it directly equates (unless you're imperialistic or expansionist).
In between, chopping down some forests (especially when you're building workers or settlers) will speed your production heaps. Riverside grasslands and hills forests are your best candidates for the chop.
And when you've got the basics set up, roads to connect cities and resources and to lead up to the doorstep of a soon-to-be enemy (if you're into that sort of thing) are pretty important.
Once you've got the basic foundations set up, that's when i reckon you should start thinking more about finessing the specific future direction of cities - building cottages etc for commerce cities and so on, farms and mines for production cities, whatever.
So i never know what to do with my worker, and i know automation doesn't always do the right thing, so i'm tryin to do something but its not helping. Other than that, what are the priorities in research?
It's hard to go wrong prioritising bronze working first, even if only for the slavery and the chopping (and the mines you get on the way). The production benefits are really enormous. You may want to pick up a relevant food tech first though if you don't have the right one for your resources. Beyond that, the wheel and pottery come pretty soon after.
Then it really depends on what you're doing in terms of military etc, but beelining alphabet is generally a pretty decent choice.
Of course this all differs if you decide to go the early religion route, but I don't really know much about all that.