Sennheiser makes very good headphones and if you want to try something different you might want to try closed-back headphones made by Sennheiser or other audio company such as AKG, Audio-Technica, or Shure. The biggest advantage of closed-back headphones is noise isolation. To be honest with you, if you like your current setup stick with it, however if you want to try something different you should definitely consider upgrading you sound source. Look up Cowon Plenue D, they usually go for less than $200, you can find them on sale for less.
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Cowon Plenue D does not have internet connection capabilities, you will not be able to stream your music. You should definitely check dedicated audio forums like head-fi, guys over there much more knowledgeable and I am pretty sure they can recommend a device compatible with Apple Music.