At the bottom of the heap were the slaves. A citizen was considered poor if he could only afford two slaves. There was an active slave market in Piraeus, the nearby port of Athens. There seems to have been a clear distinction between house slaves and work slaves. House slaves were ruled by the lady of the house. Work slaves by the master. If you were bought by the master to maintain the olive trees on the farm, then no one would order you to sweep the bedroom floors. That was left to a house slave who was probably female and under the control of the master's wife. It's reminiscent of the division of labor among the servants of, say, a Victorian stately manor.
The state itself owned quite a few slaves—like public servants but without the pension plan—and if you were one of those then you were either very lucky, or hugely unlucky. The lucky ones had cushy jobs as clerks. The unlucky ones were sent to the silver mines, where life was terrible and brief. Being a slave in the mines was the worst thing that could happen to you.
But this didn't mean the lives of all slaves were terrible, not by a long shot. There was very wide disparity, and it was possible for a slave to be better off than a poor citizen. If you were the head slave of Callias, the richest man in Athens, then your life would have been one of virtual luxury.
The metics were resident aliens, with permission to live and work in Athens, but with none of the sovereign or legal rights of citizens. If you think of someone with a green card in the US, you'd be pretty close. Metics had to register with their local deme (suburb) and have an Athenian sponsor.
There'd always been some metics in Athens, but as the city came more and more to dominate Greece, people began to flood in from the poor cities, looking for work and a better way of life. Sound familiar? It's known from funeral stele (monument stones) that the metics came from at least 60 other cities.
Metics formed much of the merchant class of Athens. With its strong agrarian tradition it was somewhat frowned upon for citizens to indulge in trade (which didn't stop the smart, successful ones) but the metics were all for making money from as much trade as possible. The metics may well have owned a lot of the merchant fleet. The Athenians certainly understood how much the wealth of the city depended on the success of the metics. One of the three top archons—the Polemarch—was assigned to do nothing but make sure the metics were looked after. It was possible for a metic to gain mind-boggling amounts of wealth. Pasion, the world's first bank CEO, started as a slave, made a mega-fortune as a free metic, and only after he had enough money to basically buy Athens was he offered citizenship—a rare honor.
Citizenship was a tightly controlled club, and during classical times it only got tighter. A law was passed that to be a citizen you had to be born of a citizen father and a citizen mother. Which strongly discouraged the men from picking up wives from out of town, because to a true Athenian, death was preferable to being a non-citizen. (Quite literally in fact...there were citizens who chose death over exile. Socrates was one of them.) Citizens ranged from the desperately poor to the very wealthy, but they all had exactly the same vote in the ecclesia.
How many of all the people were there? No one knows for sure. Calculations are usually based on estimating the number of citizens and extrapolating the rest on ratios. Herodotus in a roundabout way says there were 30,000 effectives in the Athenian army in 480BC. Which isn't necessarily true, but it's all we've got for the beginning of classical times. People have used all sorts of weird and wonderful systems to extrapolate from there, such as burials and marriage records, and averaging the number of children for those few families which are mentioned in history. Keep in mind too that infant mortality was in the 50% range. None of this is accurate!
Let's multiply the 30,000 by 4, which means 1 wife and 2 surviving children per male citizen. The mild justification is that sixty years after Herodotus said 30,000 men, Aristophanes in a comedy also said there were 30,000. Hence the citizen population was more or less static. So that's 120,000 citizens.
There appear to have been about as many slaves as citizens. That's not a total half-assed guess because there are some documents to support the one to one ratio.
There's a magic moment in 431BC when Thucydides gives the relative number of citizen versus metic soldiers in the army (5,500 metics), from which we get perhaps 25,000 metics total. Maybe as many as 30,000 metics.
So that's a total population of maybe 270,000.
But don't trust me on this. I have to see any two papers on the subject which actually agree.
What interests me intensely is that this tiny place—smaller than many modern towns—changed the world forever.