Assuming I'm being born to a humble background, I'll choose Rome after the Marian reforms. An average person was born into poverty, no matter which ancient civilization we are discussing. So the main priority as I see it, would be escaping that life of poverty.
I figure a career in the Roman Army is as good as an escape as any, so long as I'm lucky enough to not up dead in a ditch on one campaign or another. The standard of living in the Army and nutrition and health care would certainly be better on average, and if you die in battle...well I suppose a ditch in Gaul or Germania beats a gutter in Rome.
If I had to be an ancient city dweller however, I guess I'd go with the pearl of the Mediterranean, Alexandria. Alexandria during the Ptolemaic period seems a better place to call home than Rome during the Republic.