Headphones

So I'm new to headphones. I usually js buy cheap ass 30$ headphones that work pretty poorly. I want to try and upgrade a bit to some new ones. Music genres I listen to : Mostly metal/rock/punk (I listen to other types of music like jazz and shi but less often). I want it to both work outside and inside since I use it with my phone. Phone has no headphone jack but I think there's an adapter to make it into USB-C ? I ain't sure. Anyways my budget is around 100-250€ (I'm broke). Bands I listen to mostly: Deftones, Slipknot, Korn, Limp Bizkit, System of a Down, MCR, Linkin Park, Ice Nine Kills, Motionless in White, Pierce The Veil, The Cure and more