need a pair of headphones for under 100€

i only need them for gaming, I especially need to know where the sounds are coming from in the game, i would like them to be wireless with a dongle so i can just turn them on and they connect instantly, and i would prefer them white if possible. now i just use the audio from my monitor, so i'm expecting a big difference. by reading other posts i saw some people saying that i would feel the delay between the sound and thing happening in the game for under 100€, if it is true you can reccomend me wired options...