Palladium Helmet

Palladium is one chest piece and one set of legs with three heads to choose between: the Mask for melee, the Helmet for ranged and the Headgear for magic. The healing bonus behaves identically whichever one you wear, so pick the head that matches the weapon in your hand and forget about it. Which ore your world generated decides this for you anyway, since Palladium and Cobalt never appear together.

Land a hit on anything and you begin regenerating at a fixed rate for a few seconds. Hit again and the timer restarts, so as long as you are attacking, the healing never lapses. Because it is a flat trickle rather than a multiplier on your normal regeneration, it keeps running in situations that shut normal healing off, including while you are bleeding. It also does not stop if you take the armor off mid-fight, and you can see it working from the small orange hearts drifting off your character.

Anything the game counts as your damage will refresh it, not only the weapon you are swinging. Minion hits qualify, which is why a fast attacking summon like the Blade Staff pairs so well with the set: it holds the buff up while you concentrate on dodging. Critters and Target Dummies count too, so you can start the regeneration on something harmless before walking into a fight rather than waiting to be shot at first.

The comparison worth making is Adamantite, which trades this healing away for far more defense. Which one wins depends entirely on how often you get hit. Take damage every few seconds and the extra defense pulls ahead, because the trickle cannot keep up with the losses. Fight something you can mostly read and avoid, and Palladium comes out on top, since the healing runs the entire fight and repairs the chip damage between attacks. It also stacks on top of the Life Drain buff instead of overlapping with it.