Monks use whatever weapon you have equipped, they just attack with their fists. As you stated almost all the monk skills besides flick coin have amazing status effect attributes at level one so its worth it to grab them
A good stat spread would be something like 3 str 1 dex 1 con or something along those lines.
Due to the fact that both str and int are pretty much pure damage stats they don’t provide much else besides flat damage I believe it would be more beneficial to invest in some str for melee damage, some dex for accuracy,evasion chance, and critical chance, and some con for hp and hp regeneration than spending all the points on pure damage and ending up dying to any boss’s attack late game. Finally don’t be afraid to add a little spirit if you find yourself needing some more sp and sp regen since its a very efficient stat and also provides block penetration which would be awesome for a melee monk.