Coastal is often not a plus unless there's seafood, or you have the GLighthouse for semi-free expansion along the coast. Plain water tiles are bad long-term since they can't be improved. No problem of course if you can claim all the inland tiles later. Coastal is often a good GP Farm location, couple of seafood and couple of land food plus farmable grass on estuary.
You want fresh water where possible, and on river is better than lake. Fresh = extra health, and river = can build a Levee. Health will be your main problem in the later game if you industrialize.
For first cities, if at all possible, place them in the direction of nearby AIs--grabbing good resources and/or blocking off the AI. If you don't grab these locations quickly, the AI will--whereas the AI will rarely settle behing your front lines, so you can settle those spots later. Use SHenge, Monuments, religion or Creative trait to pop the borders.
For my 2nd and 3rd cities, I'm looking for one food-rich and one hammer-rich ideally. Food becomes Settler and Worker farm, and later maybe GP farm [if no better location], while Hammer builds units.
Yes, food is the #1 priority. It's much easier to get production out of food cities [via Slavery whip] than to get food=growth out of any other kind of city. I rate production as the second priority, and commerce potential as the third--it's easier to get "income" from a hammer city [build Wealth] than production from a commerce city.
I find that approach to be more flexible than more 'streamlined' ones, you have more options as the game circumstances become clearer and you need to change plans.
Once you have a bit of an empire going [say 10+ cities], you should be able to specialize a bit more, since you're starting to have enough cities to support several alternative paths.
Of course, if you have a pre-determined play style [eg cottage spam or attack attack], this doesn't really apply. I prefer to stay flexible until around Liberalism, which is the point where you're forced to select a path ahead.
If you have psycho AIs nearby, be aware that getting touching borders will make it more likely they'll attack you, so you might move your blocker cities back a tile or two if you want a quieter life. Build Walls in such cities!
Btw, if you're targeting an early religion, you may want to delay settling your 3rd city a bit if it would be good for the religion to found in your 2nd city--which it will, never in the capital. That can be great if that 2nd city is an AI blocker [the 5 culture really pops it quickly], or alternatively a good site for Wall Street--gives the option to spread the religion and build a shrine.
or should we avoid it to harness more production 
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3 
from a boring coast tile.
