I assume this is a desk setup? Do you have plans for other headphones in the future? What would be your priority, the speakers or the headphones? Since the speakers are active, it’s easier to prioritize the headphones since you primarily just need a line out to feed them.
A simple starter option might be something like a K5 Pro. The 6XX responds reasonably well to tubes, so you could also consider something like a Little Dot MkIII or Dark Voice, which could also act as a pre-amp to the speakers if you wanted to add a little ‘tubiness’ to the sound.
With your stated budget cap, though, there are lots of options depending on your sonic preferences. Sticking with entry level, Topping E30 DAC has volume control for the pre-out to control speaker volume, and pairs well with many entry level amps, such as Schiit Magni 3+/Heresy/Asgard 3, Monoprice Liquid Spark, JDS Atom, and Geshelli Archel 2 (Pro) are common recommendations. Other DAC options may not include pre-out volume control, but include Geshelli Enog, adding a DAC card to a Schiit amp, Topping D10 or D30, SMSL Sanskrit 10th, SMSL SU-8 v2, JDS Atom DAC, JDS Element II…lots of options. Many amps also have a pass thru pre-out that can be controlled by the volume knob, so even if the DAC doesn’t, the amp might.
Moving to mid-tier, a Schiit Bifrost 2 (top of your budget) for your DAC would still pair nicely with their Asgard, but also would pair nicely with many higher tier amps, such as RNHP, Liquid Platinum, Gilmore Lite MkII, or Lake People G111 as common recommendations. Other DAC options likely push budget, but could be found used, as there’s a bit of a performance gap from about $200-$600. Denafrips Ares II and Soekris 1321/1421/1521 are popular options for multibit/R2R, or Topping D70/D90, RME ADI-2, or Topping DX7 Pro for Delta Sigma. The Delta Sigma DACs tend to be more analytical and geared toward measurement prowess.
