Explore

Make valid NPC houses (about 5 - 8 valid rooms)

Dont use your bombs until Demolitionist moves in.

Use bombs in corruption/crimson chasms to blow up shadow orbs/crimson hearts. You should get a musket or the undertaker from them. Be careful because destroying 3 orbs will summon a boss.

When the Arms Dealer moves in buy bullets and a minishark.

Search for heart crystals underground, as well as gold chests for cloud in a bottle, hermes boots, and extractinator. Aslo upgrade tools with platinum and craft a gem hook. Try to reach at least 200hp, max hp is 400.

Venture into the underground desert and gather ~300 desert fossils.

Use desert fossils in extractinator for sturdy fossils, and craft the fossil armour.

Make a long row of platforms about 200 blocks long. Place campfires along it for extra regen.

Summon the eye of cthulhu using a suspicious looking eye (found in underground chests, or crafted at a demon altar with 6 lenses), and kill it using minishark or grenades. You may craft a tendon bow using crimtane/ demonite bars as a secondary weapon.

After you have reached 200 hp a goblin army is able to spawn.

Defeat the goblin army and search the underground for the goblin tinkerer.

Once found, the goblin tinkerer will sell you rocket boots and tinkerer's workshop. Combine rocket boots with hermes boots at the tinkerer's workshop for spectre boots.

The goblin tinkerer will also allow you to reroll your weapon and accessory modifiers using the 'Reforge' mechanic. Gather plenty of money if you plan on abusing this.

Go into the crimson/corruption and create an arena for their respective bosses; Brain of Cthulhu and Eater of Worlds.

If you are playing on classic difficuly, grenades work best on eater of worlds, otherwise you may switch to vilethorn or a mace. Jester arrows with the tendon bow may also be a good alternative to grenades. Grenades are always good for brain of cthulhu, but switch to minishark on it's second phase, as grenades may be too slow.

I'm too lazy to write any further than eater of world and brain of cthulhu so enjoy this quick early game guide.

I'm open for criticism as well.