Flaming Mace

You throw it and hold it out, so it hits on the way out, on the way back, and continuously if you keep it buried in something. Against the slow ground enemies of the opening hours that is close to free damage, and the burn keeps ticking while you back off and reposition.

Step into water, or let the head dip under the surface, and the flame goes out. You still have a working flail, just an ordinary one. That matters more than it sounds, because flooded caverns, the Ocean and the Jungle pools are exactly the places you would want the extra damage and exactly where you will not have it.

It holds up longer than most early weapons because the burn does fixed damage and therefore never falls off a cliff. The Sunfury is the same idea built properly, so once you can survive the Underworld, swap.