Personally, I like Monastic Archer stance the best. Not that its the most powerful (probably ranger or fighter is 'best archer', in terms of pure archery skill and feats).

But I like monks. They'll be tankier than a ranger, and have some extra utility and lots of movement. And Stunning fist is great, if not likely to proc all that often. Ki Strike strike on bows is also cool.

And just, having 'flurry of blows' leaves you with usually having two actions to do other stuff with on your turn, letting you actually have actions to use other bits and bobs you may get from skill feats, gear, or other archetypes. So you have a lot more flexibility.

So, yeah, fighter will be most accurate, ranger will make the most attacks, but I still like the monk's ability to dish out decent damage, while keeping the ability to do other stuff in the same turn.