I don't normally post here, but since this happens to be a major interest of mine (both from a Civ and general historical/worldview perspective), I figured I might as well give my tuppence.
I like the idea of starting Civ off in the Neolithic (specifically, the tail end of the last Ice Age), but I actually think the best way to do this would be to rename Ancient Neolithic and Classical Ancient (which
@UncivilizedGuy did in at least one of his Civ V mods). Most of the technologies of Ancient in most Civ games clearly aren't Bronze Age and some even predate the human race. And the Dawn of Man narrative clearly indicates a transition from a nomadic to a sedentary lifestyle (I leave aside for the moment what that would mean for nomadic civs like the Huns or Scythians), not a tribal chiefdom to a Bronze Age empire.
Although I'm not totally sold on merging Classical into Ancient; the strongest case for it for me would probably be that an exclusively Bronze Age Ancient would be rather devoid of techs if everything from the Neolithic and Classical/
Axial times was excluded. If they were seperate, I'd like to see a branching of government options in the Classical age; going from tribal chiefdom to Bronze Age kingdom is a no-brainer, but what about from a Bronze age kingdom/empire to an Athenian (cultured, democratic, pacifistic), Spartan (martial, spiritual, authoritarian), or Corinthian (mercantile, oligarchic) model? I could also see theocracies coming into play, although I think universal religion is more of a medieval phenomenon than an ancient one (be it Christianity, Islam, or Buddhism)
I'm not particularly fussed about what the middle ages are called; the key features of this era should be universal religions, trade networks, and the golden age of sieges, not feudalism, which is a very specific societal system rooted in Roman manorialism and Germanic tribal law.
I think Early Modern is a much better name than Renaissance; basically, I see it as describing everything from the fall of Constantinople, the widespread adoption of handheld firearms, the invention of the printing press, the Renaissance proper, and the Reformation until the Second Industrial Revolutio, or maybe the beginning of the "
long 19th century"). That may still be rather Eurocentric, but I'm willing to bite that bullet since the West is the only cradle of modernity I'm aware of (that is to say, modernity started in the West and spread elsewhere, although in another world it could probably have started in China, though even there I'm not so sure that, say, modern political philosophy would have developed, at least in the same way it did in the West).
I'm in two minds as to whether Industrial and WWI should be seperate; in some ways I see WWI as a sort of "final boss stage" for Industrial technology, but there may be good gameplay reasons to not have armored cars and biplanes come in at the same time as Civil War-style riflemen.
I'd favour splitting the rest of the 20th century into WWII, Cold War (which we could call Atomic) and post-Cold War (Information), with the latter extending to 2050 or so. There are enormous tactical and technological differences between even WWI and WWII, let alone WWII and Vietnam, or Vietnam and The War on Terror.
So, to summarize, I'd have;
Neolithic (10,000-3000 BC)
Ancient (3000 BC-500 AD) or Bronze Age (3000-1200 or 800 BC)
???Classical (1200 or 800 BC-500 AD)???
Medieval (500-1500 AD)
Early Modern (1500-1800 or 1850)
Industrial (1800 or 1850-1900 or 1925)
???WWI (1900-1925)???
WWII (1925-1950)
Atomic (1950-1990)
Information (1990-2050)