I would recommend the Sony TWS WF-1000XM3 on a BT connection. So far they are the ones I use regularly so long as your intention is not to be further than 3-4m away from the R6 Pro. I would not recommend ANC headphones as I find them lacking, even if wired. I would go IEM custom solution instead and for roughly $400 loose change after buying the R6 perhaps something like the AVara AV3 custom IEM would work very nicely.

I loved this review. Now I’m considering buying the R6. I’d use it at home, and sometimes on bus or train rides. I only listen to classical music, my criteria are clarity, realistic spatial staging and truthfulness regarding the timbre of voices and instruments. Would I be happy with the R6 or are there better alternatives? And is there an IEM or a headphone (possibly with noise reduction, if that doesn’t have a negative impact on the sound quality) you’d recommend? I’d like to spend about 1000 bucks for gear + IEM/headphone… Thanks again for your inspiring review!!

The R6 Pro livelier sounding and the DX160 more reference sounding. R6 has more power so if you are using headphones this might be important.

OK, and define what a good sound is to you? What is your preference?

Sound quality

What would be the criteria that are important to you?

It depends on your sound preferences but nothing too sensitive. Modern hybrid dynamic driver and balanced armature mixes might do better as they tend to be less sensitive. A safe starter would be the FiiO FH5.