Okay, here we go:
First Few Weeks
Light Operatives are the most popular, medium engies close behind. Medic is the least used class. Large Soldiers are somewhere in the middle. (see MNC, with assassins everywhere, people love playing the stealthy ninja class.
About MNC - honestly what I see the most of is Gunners, then Snipers, then Support/Assassins. And apart from myself, I've literally seen less than ten Assassins who didn't feed horribly almost every round.
As for Brink, Light everything will probably be the most popular build for the first few weeks - people are going to be SMARTing around like no tomorrow until the novelty wears off. But I can definitely agree that Operatives will be the most popular.
Third Month
Operatives are still the most popular class, but not by much. Soldiers are second, people are realizing they want to be more offensive. Engineers are third, what can I say, sentries are fun to toy with. Medics are still last, unfortunately.
I say maybe to Operatives still being in first after three months, but if they are it won't be by much like you said. I don't see Medics being in last though - I see it being ~30% Operatives, ~30% Medics, ~25% Soldiers, and ~15% Engineers. Medics are going to be rolling in the XP, so their being popular is inevitable.
Final Stage
Operatives are finally knocked out of the lead; they are now the third most popular class. Soldiers are first, with engineers next. Sorry, but I don't see medics being too popular.
That's what I envision happening, anyway.
I see a pretty even spread at this point, with something along the lines of 28% Soldiers, 27% Medics, 24% Operatives and 21% Engineers.
But I suppose only time will tell.
EDIT: Also, Mediums will probably end up as the most played bodytype, followed by Light, then Heavy. Though I doubt the gap between Light and Heavy will be too large.
God dammit why do people have to use engineer. I hate being one of the most used classes. Whatever starts to become the least used class is the one I'll be using. Hopefully I don't have to but I will do it
Is it really that important to play the least used class? Why not just play what you think you'll enjoy the most?