I'm not too familiar with DACs myself, but in terms of headphones Audio-Technicas are very good for their price range, a lot of my friends own a pair of audio-technica ATH-M50x and they are really pleased with it. They usually go for around 150. A lot of people suggest those for closed headphones that are pretty all rounders for most music genres.
That obviously depends on what you are looking for though, for that price range I'd assume you'd have some specific use for them that you have in mind. If you just simply want some good sounding headphones, then you can definitely go under 600 budget. But considering you want an external dac that isn't built in on your computer, tablet or phone, I'm sure you might want different ones

Should look into Reddit, they have entire sub where they have wikis for headphones and dac suggestions, or even post in there to ask. Hope you'll find a good ones for your own need!