Phillips fidelio x1
Yamaha hph 200
paired up with pyle phe7ab (rebranded fiio e7)
Try to find a used HD580 for classical (very similar to HD600). I'm a classical guy myself, and that was my first good headphone and still superior to others I've had since.
In particular I have a HD595 which should be very close to HD598 other than cosmetics---the 580 is better.