With your budget, I'd give the Massdrop x Sennheiser HD 6XX a look. I have about a dozen headphones including a few costing 10 times as much or more and they are the ones I reach for the most. They aren't "audiophile" headphones, in the sense that there are others that have more detail or punchier bass, or are better in other ways, but they are really easy to listen to, just a tad on the "warm" side, and super comfortable and relatively easy to drive. They are basically a rebranded HD 650 which retail for around $500-$600 if memory serves me correctly.
That leaves you with enough money for a decent DAC. A Schiit Bifrost and the HD 6XX should leave you with some money in your pocket and provide lots of enjoyment.