The sound I would like to get is,very precise,a small bit more emphasis on the bass,but not overwhelming,and definitely not dry. I don't want to spend over $550.
Thanks in advance.
K501 is out because it has very little bass. I have heard only dt880 premium 600ohm not the pro you been eying on but propably they're quite similar. I wouldn't call dt880 dry compared to k701 for example but it is definately bit analytical compared to hd600. Hd600 has sufficient bass and when I had it I enjoyed sennheiser with classical music. Hd600 are quite warm sounding headphones, something I like with string instruments. Some sort of amplification is strongly recommended for sennheisers. Same goes for Beyers and akg. Akg might look easy to drive on paper but it is infact very demanding.
For hd600 and other high impedance headphones bottlehead crack is highly recommended. I have not heard it but it has been THE thing for a while now when talking about amping hd600/650.
I had schiit vali and it was excellent for it's price. Never tried it with hd600 but it was fine with beyerdynamic and k501. I also had xiangsheng dac-01a. It was good with sennheisers, beyers and akg. However if you're sensitive to high frequences dac-01a might not be for you. I think dac-01a is bit rough on highs and with beyerdynamic it might be an issue for some people.
You should propably ask amp recommendations at amplifier section of the forum. You would propably get more answers there. Hd600 and dt880 are so popular here that you will propably find good amp suggestions on existing threads also.