Mythril Hat

Body and legs are identical whichever build you run, so this set comes down to which of the three heads you craft. The Mythril Helmet is the melee option, the Mythril Hat covers ranged and the Mythril Hood covers magic, and each one switches on a different set bonus. Making all three is not unreasonable if you are still undecided, though the extra ore is real and the mining is the slow part.

The magic hood cuts what your spells cost, which matters more here than a flat damage number, since early Hardmode mana pools have not caught up with early Hardmode mana costs yet. The ranged hat saves ammo, quiet but genuinely useful once you are burning crystal bullets and specialty arrows rather than the cheap stuff you used before the wall came down. The melee helmet pushes critical strike chance, and stacked on the crit already sitting on the body pieces it produces the largest melee damage increase available anywhere before the mechanical bosses.

The catch on that melee build is that it pays for the damage with a thin defense pool, thinner than other options at the same point in progression. The player standing in an enemy's face is exactly the one who can least afford that. If you are eating hits regularly the crit is not paying for itself, and there is a reasonable argument for keeping something heavier on until the next ore tier opens up.

This is the middle rung of the Hardmode ore ladder, and its counterpart is the Orichalcum Breastplate line. Your world generates one or the other and neither is strictly better. Both get retired once you reach Adamantite or Titanium, which usually follows quickly since the pickaxe you make from this tier is the one that mines the next. The name is borrowed from Tolkien's mithril, a light and precious metal in Middle Earth where a shirt of the stuff is a famous object. Fantasy has been reusing it, respelled, ever since.