Recommended Axe Enchantments
Axe melee hits do more damage than a sword - Sharpness V makes them hit even harder. (Sharpness, Smite and Bane of Arthropods are mutually exclusive.)
Alternative to Sharpness: stronger vs undead. Smite V on an axe two-shots most undead mobs.
Chops wood and breaks blocks dramatically faster.
Triples durability - essential for a tool you hit things with.
XP from combat and mining repairs the axe automatically.
More drops from crops and leaves. Choose Fortune OR Silk Touch.
Alternative to Fortune: harvest blocks intact (melon, bookshelves, glass).