Starting a new World
Starting a new world will always be an interesting time, to say the least. Within the first few seconds, you can tell how bad or good your pre-boss time will be. I say that because it can be very very luck-based, you could very well get everything you could want. Or spend 10 hours caving and get absolutely nothing. When you first spawn, your goal should be cutting down a few trees, and possibly crafting wooden armor before going straight into the first cave you can see. While you're caving and likely dying to a plethora of traps, bats, and zombies. You should be breaking every pot you see and looting every chest. Gold chests, are of very high priority, as these carry accessories that you need, the main one being Hermes boots. Your secondary objective are Life Crystals, as they are the only way to increase your max health. As your caving, you have likely noticed ores in your cave. Each of these ores is on different tiers and each has 2 ores that could be there. Tier 1, is copper, the tools you started with, and tin. Tier 2, is Iron and lead, which you need to make an anvil. Tier 3, is silver and tungsten. Tier 4 is Gold and Platinum, which are the ones you will be making your starting gear out of. Now if you managed to get everything that you need, (that being everything in the images below) then you are ready to go back to the surface, do a bit of crafting, and then explore your world.
Exploring a new World
Now that you've made your way back to your spawn, it's time you make a crafting bench and craft everything in the following images. Equip all of this new gear and your next goal is to find an enchanted sword. This sword is going to be the weapon you use for your first few bosses. To locate this sword, you need to find one of its shrines. Which are located in the outer two-thirds of the world. These shrines have a chance to generate a 1 tile gap above them and are almost guaranteed to spawn in your world. W hilst you're hunting for an enchanted sword, there are other things you could search for and grab. All of these will be listed under the image references heading along with an image of the item, where it will be located, and possibly a small guide on an easy way to look for said item. Once you manage to get an enchanted sword (or if you got lucky a terragrim) then your ready to proceed to the next page which is located at the top and called Pre-Skeletron.
Image References
Gold Chests
Hermes Boots
Life Crystal in inventory
Placed Life Crystal
Tier 1 Ore
Tier 2 Ore
Tier 3 Ore
Tier 4 Ore
Item's you hopefully found
Items crafted with anvil and crafting bench
Enchanted Sword Shrine, with possible Terragrim
Terragrim