how many ships / of what type would you expect the riverlands brown water navy to have? would it be organized with each lord having a small fleet, or would it be more like the vikings where every river town has a few ships for community use that the lord would then draft into a fleet as needed?

Well, we don’t see anyone but House Tully itself with a riverrine navy, so I’m guessing they’re the only one with one. 

And in terms of type, according to Jaime I they are “river galley[s]…nine oars on each side, which means eighteen men.” More, if they crowded on fighters as well as rowers. And larger sails than ours…” These are pretty small vessels, even by Ironborn standards, but against ground forces trying to ford a river, they’d be incredibly potent.