Honestly, it all depends on what type of weapon it is, and if the properties would work with it. If it's a slow weapon, you want swing speed increase. If it's a weapon that doesn't do much damage, you would want damage increase. The few variables that are paramount to any weapon would be Hit chance increase, hit lower defense, any type of % for hit harm, fireball, lightning, spell channeling(for mages), and slayer types if you hunt certain monsters.

I personally am looking for hatchets that have high damage increase, hit chance increase, fast casting, and any type of % for harm, fireball, or lightning. Also apply this statement to hammerpicks as well.