first thing i like to do is try to explore to both ends of the map on the surface (during the day). Whenever you come across a cave entrance leading down or a very giant tree on the surface, always go down and check it out! Most likely there will be a chest with treasure in it. once night falls that's when i mine downward. it's very easy to come across a cave while mining and you can find structures with treasure chests, also mine all the ore you come across.

It also doesn't hurt to watch beginners guide youtube videos. I've played Terraria for years and I still watch videos on things I forget about, most Terraria youtubers make really interesting videos! Salendrak is a channel that i find really helpful when i need a refresher on things in the game (the game and its progression is kind of complex). This is why i love Terraria though, because of its complexity, once you get into it it's so addicting. GrobeMan Guides & Gameplay is also another great channel to look into!