There are bad starting locations too.
Agree, this is probably the most important part.
Granted, some select civs can make nearly "any" start work, but in general a very poor start will factor much more than the civ one has chosen.
For instance, getting an early 5 yield tile (preferably at least 2/3 food and 2/3 production) workable from turn 1 is a very good start for me, while similarly flatland plains/grassland (or even tundra/desert) with at most 2 or 3 yields for the first tiles can be either crippling or outright devastating.
Having plenty of mountains nearby as opposed to zero mountains will also help, as well as having plenty of land to settle as opposed to being crammed in between leaders like Chandragupta and Montezuma.
Either way, the hallmarks of a good player is ability to identify both the potential of his surroundings, as well as identifying (and ability to achieve) key "breakpoints" in the game that will tilt the game in one's favour.
Examples of these can be when you get an outright terrible tundra start with no production, but you happen to have a good productive location right north of your capital, and your capital is otherwise spawning next to Fountain of Youth.
A good player will recognize that his start is terrible and that he needs to settle the good land up north immediately in order to not fall behind, instead of trying to churn out scouts/builders/settlers with essentially no production to back it up.
That player will work the Fountain of Youth for 7 turns only (netting him 28 faith and a pantheon assuming standard speed), which he will use to immediately take the free settler pantheon to settle the good land up north.
He has now achieved a breakpoint, which if he didn't identify early on, he would be stuck for a long time on a horrible start trying to catch up to everyone else.
He will then again of course switch out of working the Fountain of Youth immediately after, since all that faith and science serves him no real purpose anymore after reaching said breakpoint.
A poor player might similarly try to work the food tiles from the start (giving him a very slow start), or be stuck working the Fountain of Youth for the rest of the game (since he never gets more population), but sticking to his choice because "a wonder is great, I must work it".