Probably some of the oldest tricks in the book, but when starting a new world,
Go to one side of the world to try and get an Enchanted Sword/Arkhalis, Go to the Dungeon and hope that a water bolt spawned above 100' Underground. (Very OP)
Or if your world is Corruption, get a few bombs and break a shadow orb(100% chance to drop a musket first time) which is helpful because that will do two things:
1, be then able to have the Arms dealer move in, and 2, have a 31 base ranged damage weapon super early game. (Not so useful if you're playing with a class, such as Mage or Warrior)
Those are my life-hacks, getting good weapons early game.