I am being intentionally vague here, because the point of the game is exploration and discovering stuff yourself, not having it spelled out for you. But I will give you pointers on what to do next.

You haven't activated Hardmode yet, so gold ore is the strongest you can find underground. Try fighting the Eye of Cthulhu next. It may randomly spawn at night, or can be summoned by using a Suspicious Looking Eye, which can be found in chests or crafted. (Hint: the EoC is a giant, floating, disembodied eye, making it effectively a giant version of which nocturnal monster? And what do they drop? Ask the guide for crafting recipes.) It will drop Demonite or Crimtane ore, depending on if your world contains Corruption or Crimson respectively. On their own, these will allow you to create a new tier of weapons.

The next step up is exploring the Corruption or Crimson and fighting the biome boss by breaking 3 Shadow Orbs/Crimson Hearts found in the underground there. (Hint: Ebon-/Crimstone is impervious to even a gold pickaxe, you will need something with more destructive power). They will drop the same ore as the EoC, and a secondary material required for the next tier of tools and armor.

Also

After that, go explore the (Underground) Jungle. There you can find materials for a set of mage's armor, as well as more of the regular ores, and neat stuff from treasure chests. (Hint: Make sure to take a ranged weapon, to deal with a certain highly dangerous enemy down there.)

Breaking at least one Orb or Heart will have a chance to spawn a meteorite each night, landing somewhere on the overworld and granting access to (duh) meteorite ore. Mine enough of that for the next tier of gear. (Hint: Be careful, meteorites are burning hot, and seem to attract unpleasant company).

Around that time you're able to enter the dungeon, but you'll have to defeat its guardian first. The Old Man roaming near the dungeon's entrance will tell you what you need to know. (Hint: Wait for the night.) In the dg, you can find a few useful weapons and gather Bones from the enemies, that can be used to create a ranger's armor.

Once you accomplished all that, it's time to dig straight down. Literally. Find an accessible spot near your base and start digging, creating a "hellevator". (Hint: better find ways to deal with water and/or lava falling into your hellevator). You'll immediately recognize when you reach your destination. Make sure to gather one of the forges found there, and as many of the native flora as possible. Here you can find the final pre-HM ore that gives (obviously) the best tier of weapons, armor and tools. Ideally get a full set before proceeding. (Hint: the ore is likely surrounded by lava, and burning hot to the touch. Ask the guide about uses for the plants found in that same area to find a way around the heat.)(Also if you have all four of the Swords found from here, the Jungle, the Crimson/Corruption and the Dungeon, you can unite them at an altar of evil to obtain the strongest Sword ).

I may be needlessly cryptic, esp on the last part, but as I said, discovering stuff yourself is a way more rewarding experience. (Though if you find that stupid and want plain answers, just say so, and I'm happy to oblige with those as well.)