I am waiting for my set and I will buy a new amp at the same times. I was new in the audio world, but I read and saw videos online. I was wanting to enter the headphone for cheap. So I purchased my first headphones who was the Fostex T20RP MK3. At the same I purchased the dac/amp combo Micca Origen+. The headphones are really hard to drive because of their low sensitivity and not their 50ohms. But, volume was still fine. It's get more loud than I need. What I learn is that they are not driven at their best. To conclude, what you should know is that gain=volume and more power= better to move the drivers.
Also, a dac is the way to convert digital music( binaries 1 and 0) to analog( electricity to airwaves that you can ear ). The the Dac just send a low electricity signal so, you need an amp to amplify the signal to drive your headphones/speakers.
So, with all that said, a better dac gets you a more accurate signal and a different sound, and a better amp can gets you more power to drive, better power delivery, different gain stage and a different sound tuning.
So, for the 6XX, a cheap dac/amp combo or your motherbord may get your headphone loud enough, but for the best results, go with something stronger. For your price point, maybe the Fostex HP-A4, Aune X1S dac/amp, the Schiit audio magni/modi etc. For something stronger, maybe the Schiit Jotunheim amp or dac/amp(100$ more) or the Aune X7S amp. Remember that they are 300ohms! So it takes a lot more power to move the drivers than a 32ohms to go at same volume, (but, it's better, because it moves the drivers faster so tighter bass etc.)
For this headphone, a balanced cable will be even better. Usually with a 4pins XLR plug termination or 2.5mm trrs or even the new Sony pentagon 4.4mm connector ( depend on your amp) This will get you more power than the 3.5mm/1/4inch connection also called : single ended or unbalanced.
The Aune X7S and the Schiit Jotunheim have the balanced and single ended connections.
Finally, if you want some fun with them, a tube amp will be. It adds more soundstage etc. The Darkvoice may be a good choice.