I like the terms Aristocrats and Commoners, though not Proletariat, because even though it sounds better than "tribesmen", it doesn't really fit the role. It's supposed to represent "barbarians and uncivilized parts", not "dirt poor populace".This thread is about the patrician/plebeian divide, which is why I believe stratigos honed in on that. The use of 'Free Men' and 'Servile Men' would be incorrect as well for the reasons you mention, however they weren't the focus of this thread so no one is commenting on it.
I understand what you're trying to say - that there was a difference between simply being 'wealthy' and being 'senatorial' - but the objection is purely to do with your use of the word 'plebeian', since that category of your list would have also included patricians.
Back to the topic, though. IMHO, if you want a system that works for as many cultures as possible within this time period, this is what I would suggest.
Aristocrats - represents philosophers, lawyers, statesmen etc - anyone who can afford to think rather than work. Provides research points and trade income.
Commoners - represents the vast majority of the free populace. Provides manpower.
Proletariat - represents free populace that owns little or no property. Provides only a small amount of manpower and tax income.
Slaves - represents slaves as well as any other servile position. Provides tax income.
Then you could have laws, traditions, events, etc which provide modifiers to the above. For example, aristocrats could seize public lands for their own use, converting some of your Commoner pops to Slaves and Proletariat. You could then enact laws to reverse this at the cost of reducing Aristocrat output. And/or you could enact laws to increase the manpower output of the Proletariat...
I think you can see where this is going.
I would choose something like "villagers" or "countrymen" for this type of pop.