Well I've played a couple test games, only during the early portion of the game, and I have to say the barbarians are a royal pain the butt. I have a feeling a lot of people are going to be complaining about them in the first spoiler thread. You pretty much need to build a very strong military at the start and actively search for barb encampments, even sacrificing mp to do so. You want to get all those little camps destroyed before they start spewing forth tons of horsemen. I'm not even talking about once you reach the middle age, the horsemen before that are just as much of a pain. I think most people are used to roaming barbarians, and restless is just so much worse.
But be careful with your treasury at the start of the middle age. It's really hard to prevent a barbarian uprising from sacking one of your towns. So you should make sure to get your iron hooked up before that and spend all your cash on upgrades before you lose it. In my first test game I lost 700 out of 800 of my gold because a horseman uprising sacked one of my far off towns. I hadn't hooked up my iron yet so I had a lot of warriors that I couldn't upgrade anymore. With the large number of civ's, and all of them having contact nearly from the start, you'll be in the middle ages before you even realize it.
I'm actually contemplating using vanilla civ3 instead of ptw just because the barbarians are a lot easier to deal with and even take advantage of in vanilla. In PTW the barbarians put a much higher priority on your workers than your towns, unless your town is undefended of course. They will circle all the way around your towns to sneak attack your workers. They will run away from any of your military units that are on defensible terrain. So chasing down a barb horseman with your warrior is a challenge, since the only way you'll catch up to it is by moving onto flat terrain, then the barb horseman will just kill you anyway. The barbs will pillage all your terrain before attacking a defended city. They will make sure to end most of their turns on mountains. You can usually still defeat them on mountains with the 100% combat bonus but it's not guaranteed by a longshot. Be prepared to lose quite a few units to barbarians, hopefully not your workers and settlers.
edit: At least the celts are militaristic. Those cheap barracks are a god-send. Religious is very helpful too, cheap temples will give you a huge boost to culture & territory right from the start.