you can buy a usb soundcard for cheap which will give you a mic jack and a headphone jack. that will solve your issue.
likely the best over ear headset you will find under that price are the gamecom 380's for 22gbp.
or, you could have a look at any of these in ears http
/thewirecutter.com/reviews/best-headphones-under-30/ or something similar which may come with a microphone. generally though they will be omnidirectional microphones which may pick up on lots of background noise.