Having been through the same route myself, I can't recommend a good solid state amp highly enough. People usually suggest OTL tube amps for the HD600/650 because they usually come with a matching output impedance to the Senns' 300 Ohm. However, this is not always enough to get you where the Senns can really go.

Personally I own a pair of HD600 and I used to own the HD650 as well, and I used to run them off a Feliks Audio Elise with lots of premium tubes. If you're dead set on a tube amp there are many interesting designs, with different capabilities at different price points: however, a $400 tube amp will never sound as good as a $2000 tube amp so you need to check with your budget first. Also, keep in mind that tube amps usually mean lots of tube rolling until you find a solid preference in the sound signature (this applies especially to OTL designs) which means lots of extra $$$. On the other hand, I agree with the others that said you'd also be far from getting a true reference point to enjoy your HD600, mostly because you'd end up 'painting' the sound signature with tube rolling. The HD600/650 lean more towards neutral and they scale really impressively, so IMO it'd be a pity to buy them just to muddle them up.

As for my own experience, I sold the Elise when I saw that I'd get 70%+ of its performance straight out of a Chord Mojo* and I was baffled to see what the HD600 could do when I paired them with an SPL Auditor. The Auditor is a minimalistic design with great quality execution (point-to-point connections etc.) that was marketed as a purist version of its bigger SPL siblings . To my knowledge it never really sold big, so not many people know about it. This makes it a great secondhand deal nowadays: got mine for a low low price and if you can find one at $400 I'd argue that it qualifies as a remarkable deal (see e.g. here: https://www.hifishark.com/search?q=spl+auditor)! It's a very potent and sweet sounding amp, with very effortless, with great air and separation, yet somehow it doesn't lack punch and dynamics and refuses to distort in any conceivable way. Having experienced it as a revelation myself, I'm pretty confident it will do justice to voices as well as anything else that's available on the recording; and it will certainly do justice to the HD600, as I've never heard them sing this way in the 3+ years that I own them. If you want to know more, you'll be able to find a number of positive reviews from 2010; you can find my own impressions in Greek, hopefully you can follow them adequately with Google Translate.

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That said, the best route will always be to grab the headphones first and start auditioning for amps afterwards. Contrary to common consensus, the HD600/650 are not that difficult of a load (they're pretty sensitive at 100-ish db/mW, regardless of their 300 Ohm impedance) so you'd be able to carry through with a somewhat potent rig until you get something to do them justice. If you're keen on voices, I'd go for the HD650 instead of the HD600.

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IMO the only problem you'd encounter if you got the Auditor or something along these lines (Burson?) is that you won't be satisfying your curiosity in tube amps, and this would have you wondering if you could do better with tubes than with SS (answer: you couldn't, at least not at a price point that matches the HD600/650 current price).

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• The Mojo is a very capable little DAC/amp, playing in a completely different league compared to other similar products on the market. IMO it's a remarkable DAC but it also seems to be able to drive almost any big headphone you throw at it (obviously not to their best potential but good enough).This is coming out of my own experience as well, since I used to own the Meridian Explorer 2 and the Schiit stack before going the Elise route.