My favorite headphone under $40 is the JVC HAS160. It is around $11 on Amazon. It is closed supraaural, however it doesn't isolate so well. If you are willing to spend $41, then look at the Sennheiser PX100-ii. You can get the Koss KTXpro1 for around $15. If you don't like how it looks, you can get the Koss KSC75, which has similar drivers, but no headband, so the bass will be less. Another choice is JVC HAS600 for around $30 on Amazon. . It is on the ear for some people, while for those with smaller ears it is over the ear. It is an extra bass headphone, so the midrange is somewhat recessed as are the highs.It is a closed headphone.
You didn't mention it you want a closed or open headphone, and if you want a neutral one or an extra bass one.