Headphone suggestions needed

I'm building my first high-end headphone system and need some headphone and dac suggestions based on my current setup.

I went about this backwards....I bought the amp first (a good deal fell into my lap).  I bought a Cary HH-1, a tube hybrid that uses 6922 input tubes.   What headphones would pair well with this amp?  What DAC would you recommend?  I would like to have a few options to put on a short list to either demo or research in further detail.  My budget for now would be up to around $1000 for the dac/headphones, new or used gear.  Right now I'm listening to sennheiser momentum 2 wired overear, and for the most part...I like them.  I also have a bottlehead foreplay tube preamp that can be used.  I just don't want flabby bass or shrill highs, something with accurate bass, great mids, and airy highs that aren't fatiguing.  Grado? Sennheiser? Audeze?  I will be using my laptop/tablet as a source with tidal and roon.

Thanks