Fradow summed it up. In more detail:

In the shallow parts of the Clockworks (Tier 1), monsters deal mostly normal damage. As you go deeper, monsters increasingly deal their preferred damage type (e.g. piercing for slimes). But even on Tier 3, there is a lot of normal damage coming at you. So you ideally have a normal+piercing armor set, a normal+elemental armor set, and a normal+shadow armor set. If you can't (or don't want to) afford all that, then try getting a general-purpose set, such as Divine Veil with Skolver Coat.

Each monster family is vulnerable to one kind of damage, resistant to one kind of damage, and neutral to two kinds of damage (including normal). If you carry only normal weapons, then you will deal moderate damage to all monsters. At the other end of the specturum, by carrying all three non-normal damage types, you can deal huge damage to 6/6 of monsters. In the middle, by carrying two non-normal damage types, you can deal huge damage to 4/6 of monsters, and moderate damage to the other 2/6.