60the early mage helmet
For a pre-Hardmode mage this is close to the best thing you can put in the helmet slot, because it gives damage and crit at a stage when most headgear gives one or neither. What it does not give is defense worth counting. That is the right trade for a class that kills things before they arrive and the wrong one if you are still learning a boss pattern.
The set it belongs to is the gem robe line, and its bonus is a block of extra mana rather than anything offensive. Mana capacity matters most before you have regeneration accessories, since it decides whether you finish a fight or stand still drinking potions halfway through. Once meteor gear is on the table the mana problem mostly solves itself and the damage is the only reason left to wear this.
Acquiring one is the annoying part. The traveling merchant carries it at random, so you either check his stock every visit or take the wizard hat instead if one turns up.