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.

I had an investigator with medic and eldritch archer archetypes. Basically going for one huge hit per round with strategic strike and enchanting arrow damage, with higher hit chance because if my devise a stratagem roll is bad i can just chose to attack someone else and have another attempt at getting a good roll. If i used pursue a lead on the target i could even use an eldritch shot and strategic strike because devise a stratagem is free in that case. And if there is no other target i have my battle medicine. It was also a useful character for out of combat healing, although that is kind of besides the focus of the post.

I like the idea of a mounted archer, I tried it with a gnome druid on a llama. I could have build him a ranger but I wanted to take Eldrich Archer later on. He was pretty effective, with the llama speed he kept out of range and could damage with the bow or spells. Sadly that campaign didn't last long, so my experience is from the first 3 or 4 levels.

A similar idea I have now that Guns & Gears gave us the gunslinger is making a dragoon inspired character. No, not the Final Fantasy class, the historical mounted infantry unit. I would probably make him a spellslinger and maybe a beast gunner since I like casters.

I'm a relatively new player, but I've been running a flurry ranger with a composite shortbow with rogue archetype. Being able to make 4 attacks in one round with a high enough modifier to be relevant is fun

It requires a bit of setup, but I really like a lizardfolk ranger setup that uses the Druid archetype for the lightning focus spell, Ranger's Bramble from in-class feats, and Terrain Advantage from lizardfolk feats to really tank someone's AC before firing off a volley.

I really like Fighter with the Arcane Archer archetype. I think it expands on what fighters can do by "default" very well, and critically gives them tactical options to a ranged martial build. Plus, as a fighter you are just super effective at dealing consistent damage, even more so at range.