Did you ever figure out what model and year? That would help a bit.

As for the maximum tire size, if we ignore the rims and brakes for a minute and assume it's got the original fork it should handle some pretty wide tires, i.e., 38mm + fenders + room to spare.

If it has calipers, then the size of the caliper will become your limiting factor. If it has unusually narrow rims, that could also be a limiting factor on the very wide tires. It's the inside width of the rim that dictates the maximum and minimum tire width to use with a given rim.

As for how large of tire you'd want, once you get past the component constraints it's a question of how much tire do you need? What's your total combined team weight? Will you be riding off-road on gravel paths, tow-paths, etc? A 32mm tire might be more than adequate and, as for "speed", it doesn't matter how fast your going if you need a 35mm wide tire just to keep from flatting when you slam into a pot hole or crack in the road from frost heaving.