Level 1-51

Instruments until you reach level 70 have different bonuses depending on the instrument you pick. This will change once you reach level 70, so until then your choice of instrument might not just depend on it's sound. Your crafted instruments are available to you at 20, 30, 40, and 51.

Here are some instruments that you can get from a woodworker at level 20.

As you can see, each instrument offers different stats. At level 20 you will probably find yourself using the Drum over anything else, and if you need to heal a Theorbo.

When you reach level 40 there is a slight change to the instruments. You have to choice of choosing damage type. You can choose Beleriand, Ancient Dwarf-make, and Westernesse. Different types of mobs are less resistant to a different damage type, in end-game you might find some mobs that can only be hurt with Westernesse damage. Most people however choose Beleriand for their damage type.

At level 51 is the last crafted instruments available to you and require Acquaintance Reputation with the Galadhrim. These are the elves of Lothlorien and you only have to do a few quests to get this reputation. After 51, there is a noticeable gap and your next instrument will not be available until level 70.