Hey there Vaiels, yes you definitely want a DAC to accompany the amp in order to get the most out of the audio file to the amp...
Was in the same boat last year shopping for a decent budget amp for the 650's. Ended up getting the NuForce Icon HDP used($300 amp/dac)
Unfortunately a few months after getting the NuForce(used) the DAC fried while plugging it in, and it ended up being 2 months out of warranty. Lots of people have good luck with this amp and enjoy it with the 650's... It was enjoyable but didn't last, and couldn't find any replacement electronics to revive the unit.
After a bunch more research, ended up grabbing a Maverick TubeMagic D1 Plus /w upgrades. Immediately impressive. I didn't get a chance to do a side by side comparison, some may argue, but I'd easily recommend it over the NuForce for the 650's any day. The NuForce in my opinion barely kept up unless it was played loud, and felt muddled in the lows and didn't have that musical sparkle of higher end equipment, these cans totally lit up with the tube and plays much better at all volumes. I have a preference for low volume listening.
Can't speak for the Schiit amp/dac, haven't had a chance to test drive them but hear that the upgraded Maverick D1 Plus stands up with their higher priced models.
Also would love to try the Audiogd amp/dacs, hear great things about them too for their price.
If anything, here's a few ideas to run with and research.
Have fun with those 650's they rock!! Cheers!