Build on a hill. Preferably a hill with a Luxury Resource like Gold/Copper/Salt/Silver or a bonus resource like Sheep.
Especially for your expos, settling on hill is good as it gets you an extra hammer. It is remarkable how that helps early. Every other non-special has exactly the same yield -- except hills give you one extra hammer.
Settling on mining lux is particularly good but
not salt. You loose a yield. I think it may be the only lux that you want to avoid settling on top of.
I wouldn't go that far. Another factor that should be brought into account is how much forest you have around your new city. I'd rather settle on a flat land and be immediately adjacent to a few forests then be 2-3 tiles away (assuming resource access is the same). If I can chop 2-3 forests immediately that's the equivalent of a free ancient era building.
This is very good advise, as those early chops are so helpful. If the chops let you build a watermill and workshop, then even with zero hills the expo can be okay.
The main downside to settling on anything, even if the yields show no loss, is you lose a good tile to work, which is why I favor tiles I couldn't be working for a while anyway if I do it.
This fact drives my decision making quite a lot actually. If I can help it, the
only non-special I will plant on is copper/silver/gold -- because why give up a tile? You would never
work a flat desert tile (or unimproved marsh) -- but if you
settle that spot it gets the same yield as a city on plain or grassland. So settling on flat desert nets the city one more tile to work.
I'm fairly certain most players will move their capital at least a few tiles before settling
I think it depends on your definition of “few”. I would wager that most (i.e., half or more players) settle by T1. The map algorithm gives you an above average spot initially. It is very much a case of diminishing returns the longer you wander. Plenty of exceptions of course, lots of anecdotes, but the math heavily favors SIP over even a one turn delay. Even knowing that, I resist SIP in most games, but settle by T1 in nine out of ten games I would guess.