Pre-bosses

• gather 50 silver, get the merchant to move in
• gather 4 gold, buy mining helmet
• build a skybridge out of hay and get the items available from the first three floating islands
• gather iron, silver, and gold pickaxes and armor

Corruption / Crimson

• collect Shadow Orbs by using explosives
• battle the Brain of Cthulu, if you're strong enough
• once so, use the resulting ore to create Crimson armor / Shadow armor

Skeletron / dungeon

• kill Skeletron and explore the dungeon
• find the Cobalt Shield to eliminate knockback
• find the Skeleton Key

Jungle

• gather useful chest contents

Underworld (hell)

• gather Hellstone

Preparations for entering Hardmode

• perhaps gather the items for Night's Edge sword

After entering Hardmode

• Build up your pickaxe so you can mine Adamantite/Titanium, then collect enough for Adamantite/Titanium armor.
• Collect Soul of Light from Wyverns to craft Wings.

Before The Destroyer

• craft the Onyx Blaster
• farm Dark Shards from Corrupt/Crimson Deserts

After The Destroyer

• craft the Megashark
• farm sharks and get 5 shark fins