The DT860 is one of the beyerdynamic models that needs a high impedance amplifier output in order to sound its best. Jan Meier rates it as "one of our favourites" with 30 - 120 ohms in series, and his is an opinion I have learned to value. Jan will sell you an Oehlbach adapter (120 ohms) you can connect in series with the headphones. Another possibility would be the adapter cable (75 ohms) that turns an Etymotic ER4P into an ER4S. They might even sound OK if fed from the headphone output on a regular stereo amplifier, which usually has a resistor in series.
I have both the DT880 and DT931 models and find them wonderful for classical music, especially opera. When correctly driven, they both have a bright but airy presentation without an over-emphasised bass. I have not heard the DT860, but if it's in the same league as these other two, as Dr Meier suggests, it would certainly be worth a listen.
That said, my personal favourites for classical and opera would have to be the DT880 and Sennheiser HD650, with the AKG k501 a close third (provided the recording is not aggressively bright). The DT880, by the way, does not benefit from a high impedance drive, nor do any of the Sennheisers or AKGs.