My personal recommendations on reinforcement

This is just a personal thinking on reinforcement efficiency.

Result first: reinforce your bow.

Reason for this,

1. Up to +35 it is acievable with S rank smith skin and luck. However, above that, you have to invest your diamonds to prevent your reinforcement lvl to go down since the success rate gets extremely low. Therefore, you need to decide which weapon/class you want to invest your diamond.

2. Currently, due to the balance patch, mechanical archer shows extremely high efficiency in dungeon and decent performance in yard (only if you master additional skill electronic turret). Since you obtain transfer scrolls (transfering links, awaken, reinforcement, etc.) and high rank weapons from dungeon, mechanical archer is a must for farming these. Mechanical archer can also be a good replacement of orb master in yard.

3. Carpet bomber, other 4th class archer, shows great efficiency in challenge top, where you farm the ingredients to fuse scrolls and weapons. Carpet bomber also shows decent performace in diasius tower and boss raid.

Therefore, reinforcing 1 bow and reinforcing it all the way is most efficient in my opinion since you can share that bow between those two archer class. It is not late to switch to other class after you earn the highest rank weapons since you will have plenty of reinforce transfer scroll by then.