I would recommend some planar magnetic headphones. Although I never listened to them personally, I read that they are truly amazing. Audeze, Hifiman, oppo are some of the companies that I can think of. These headphones should be paired up with an amp for true audiophile grade performance but you can also opt for low impedance headphones if you are looking for a mobile setup.
You can also go for open back headphones. Sennheiser is the first company that I would recommend because of their signature sound quality and well renowned sound signature. Beyerdynamic and audio technica are also awesome.
If you can decide on what to get i.e wired or wireless, open or closed back then you can decide on the company and product.