There’s so many options to consider!
Wireless or wired. Wireless. Does not mean a reduction in quality anymore. I’ve got a wireless DAC that sounds amazing (Qudelix 5k, £100). I collect that to my sennheiser hd650’s and it’s truly astounding, some tracks I have heard many times before sound very different due to the detail that I can now hear.
Open vs closed headphones. Open are typically better sounding but leak sound and you can hear your surroundings. Closed headphones generally have less soundstage but you hear less of your surroundings and those near you won’t hear your music.
You can also get noise cancelling headphones which are closed back. These are great for steady noises such as engines or air conditioning and will reduce other noises such as general office noises. But, generally they won’t sound quite as good as another headphone costing the same as they have to include a lot of technology to cancel the noise. Sony or Bose are the only two with considering in the noise cancelling imho, but you will need to pay £150 or more.
Another thing to consider is your source of music. Plugging into the headphone Jack of a phone isn’t going to give the signal quality a really good headphone needs. Some headphones are also less sensitive so need more power to drive them, again a phone doesn’t output much power, but I found that the apple lightning to 3.5mm adapter just about powered my hd650s. But I was close to max and it wasn’t loud.
edit
If you either have a decent source with good power, or don’t mind spending a bit more to get something like the Qudelix 5k, the sennheiser hd650s will give you amazing hifi sound. They are used in many studios to master tracks and off for some reason you didn’t like them you could sell on at not much of a loss if you bought a good pair
second hand. I got s bargain, but you could get a good pair for around £200.
If noise cancelling headphones seemed what you want , I would recommend finding anew pair of Bose qc35 on eBay for around £150, or a new pair of Bose 700s on amazon for a little over 200. I got mine from amazon Germany for about 210. Lots recommend Sony’s, but I discounted them once I found that you can’t get replacement ear pads from Sony and they were more often found to be uncomfortable vs the Bose