Well here's a few tips to get you going:
- Build a house so you're protected from the zombie invasion at night. You'll want to craft an anvil, workbench and furnace. You will use these to craft items. Make some room for chests too.
- Start collecting ore to make better armour, pickaxes and so on. The tier goes copper -> iron -> silver -> gold then you have various ore above that such as demonite and hellstone. You don't need actual recipes to craft new stuff, just the materials. Armour, pickaxes and so on usually just need a certain amount of smelted bars. Potions for example are a bit more random in the materials used though so you may want to refer to the wiki for such things.
- The best stuff is found in chests although the rarest item in the game (sunfury) has a small chance of dropping from a creature in hell. I'm not sure which but I just randomly found one in my inventory
- Once you meet certain criteria, merchants will move into a suitably built house you have made for them. Check the screenshots in this thread to see examples.
There isn't a single objective within this game. You do what you wanna do within the limitations of your character.