Well I have a Sennheisser HD600 which is very similar in to what you have.
Since you asked about "sounds good", I will talk about what I think it sounds like.
*** Note: my listening impressions are purely subjective and no double blind tests were performed. So definitely consider them subjective impressions. ***
I haven't found a better amp than the Emotiva Basx A-100 to drive these with the jumpers engaged to deliver its max power. They also sound great witthout the jumpers engaged but imo it sounds more dynamic to my ears so definitely worth engaging the jumpers. Engaging the jumpers lowers the output impedance on the amp from 220 ohms to less than an ohm. It also unleashes a completely ridiculous output power of 1300 mwatts/channel @ 300 ohms impedance - which is what your HD6xx operates at I believe. Yeah try find that power elsewhere. (You won't.) Having said that, you don't actually need such incredible power figures to sound good. But it's nice to know you have it. Also I haven't ever found my Senheissers sounding good with an amp that can manage less than 100 milliwatts of power at 300 ohms - even if it's enough to get it very loud. The only amp that comes close to the HD600 that I've tried is the Mytek Liberty DAC/amp.
The experience I get with these is that there is pretty much exactly what you are hoping for when you spend a bunch of money on a headphone amplifier. You've heard of the Sennheiser veil? This gets rid of most of that veil, throwing the headphones around with little abandon. There's also lots of detail, extended bass from what I'm used to, a quickness to dynamics, and an overall "large, open" sound.
You probably want to spend about a $100 for a DAC. I reccomend getting a DAC that has a volume control because with jumpers engaged (direct drive) you don't have a lot of play on the volume control. So I mainly use the DAC to control the volume and leave the A-100 with its volume set at a max (low) volume.
Some options on the market are : The Schiit fulla 2 does have a volume knob so that's pretty nice. Not sure how well it measures.
You can get Emotiva's Little ego or a Schiit Modi though they don't have volume knobs. The little ego does use an analog resistor ladder however to change volume. To change the volume you have to do it manually through your computer. So you may or may not like that. You can also spend $50 and get a Schiit Sys which is a passive volume control if you don't want to deal with not having a volume knob.