It depends, if your aim is good and you have a mixed playstyle between offensive and defensive i would recommend Bow 2
If your playstyle is more aggressiv and you're a good pooster with quick reflexes I recommend Bow 1. The only weakness is the range of Bow 1 but it can be closed in with good movement and poosting.
If your playstyle is more defensive and you have good aim I would recommend Bow 3 so you can snipe with it.
The Bows 4, 5, 6 (crossbows) are just weaker versions of the Bows 1, 2, 3 in my opinion.
There is no "best bow" it depends on what bow you can use the best and what is the most fun for you!
I use Bow 1, 2, 3 depending on the map
For example:
I would use Bow 1 for:
Alleys, Castles, Tombs, Graveyard (maps with a lot of obstacles)
Bow 3 for:
Hills, Forts, Desert, Fields, Ruins (maps with good snipe spots and open terrain)
Bow 2 for:
The rest, for example Halls, Arch, Gatehouse, Towers (mid ranged maps)
But its just personal preference. You CAN use Bow 1 on Desert but the small range will definitely make it harder to approach enemys.
If anyone read this entire post: congrats you have a good attention span! xD