Moving the HD 600 discussion over here to avoid going too far off-topic on Resolve’s headphone ranking thread…
Tube amps can look intimidating but they don’t have to be. It can be tricky seating the tubes in their sockets, and the tubes get hot. But besides this and making sure you use only the tubes recommended by the manufacturer, there’s little to worry about. Tube rolling is entirely optional. The stock ones will have been selected by the designer/manufacturer to work nicely, possibly ideally for the amp (while keeping the cost of the amp reasonable).
You’ll need to burn in the new tubes, typically for 20 or 40 hours. But you don’t need to do anything special here - just play music and listen to it as you ordinarily would while the tubes burn in. The tubes may make some odd sounds at first, as they warm up and settle down - the occasional hiss or pop - but once burned in and up to temperature, they’ll come to sound great. Each time you use it, you’ll need to give the amp 15-20 minutes to warm up before the sound becomes ideal. I avoid using tube amps if I’m only going to be listening briefly. I understand that turning them on and off again repeatedly stresses the heaters and will shorten the tubes’ lives. I usually turn the amp on and leave it on when I know I’m going to have a good listening session for a couple of hours or more.
I’m not sure what your budget would be, but for the HD 600, some good amps might include the following:
The ZDT Jr.
This amp is out of production now. It usually comes up for sale second hand. Don’t pay more than $350 for it, and beware of units that suffer from a hum. Ask the seller about this. The ZDT Jr was sold by Drop. Drop offered to fix those amps that suffered from a hum, and the ones that were fixed have a white dot on the back. The ZDT Jr. has a nice, slightly warm sound to it. It has some of that tubey gooey goodness. It does help with improving the staging of the HD 600. It’s not the best amp for the bass response; it’s a bit flabby and loose, but this shouldn’t be a big problem if you like the HD 600. It’s not an issue for me.
SW51+
This amp is also hard to come by. It was made by a guy in Russia as an exclusive for members of the SBAF forum. He may still be taking orders, I’m not sure. He makes them in periodic batches, and each batch can take several months to be produced and shipped. Used, the SW51+ sells for $350; new it’s just over $400. It’s a more neutral amp than the ZDT Jr., and doesn’t project as large or spacious a soundstage, but it has a lovely tuning and makes for a wonderfullly engaging, immersive listen, one that’s full of detail and timbral richness. I also like it’s staging with the HD 600; it makes for excellent imaging and separation and layering, and it has a nice effect of spreading the stage a bit wider. It has a gentle sweetness with the HD 600 that’s tremendously appealing. It’s also an amp that delivers a rich midrange presentation, which makes it a pleasure to listen at lower volumes.
The only other tube amp I’ve heard with the HD 600 is the Drop Cavalli Tube Hybrid but while it’s decent, it’s out of production, and you do better with other alternatives. Another tube hybrid amp (i.e. one that also has solid state components), is the
Vali 2+
This is an affordable, highly regarded amp, one that is said to pair nicely with Sennheiser headphones. It is famed for punching well above its weight and for having a lovely sound to it. For $150 it’s well worth a listen. You can always send it back minus a 15% restocking fee (and shipping expense, of course) within 15 days if you don’t like it. I’ve not heard the HD 600 with it, and I’ve only heard earlier versions, but it’s a great little amp and might be ideal as a starter one for you. You don’t have to worry about getting matching pairs of tubes, for instance. I’d recommend starting here, with this amp.
Other tube hybrids to consider are, potentially, the Schiit Audio Lyr 3 and the Monoprice Cavalli Liquid Platinum. They might work well for you but I’ve not heard them. @generic can comment on the Lyr 3 pairing, I think. (The Monoprice goes on sale for ca. $500 every once in a while; don’t fork out the list price of $800 for it, much less the current list price of $1K; Monoprice is constantly shifting the prices online).
The Schiit Valhalla 2 might be another more affordable option but it’s known for being neutral and having a dry treble that might not synergize well with the HD 600. The Bottlehead Crack DIY amp might be an option - again, @generic can help here - but you’ll either have to build it yourself of buy it from someone who has (this might entail some risk; check the seller knows what he or she is doing).
Higher-end tube amps include the Quicksilver, which has been getting positive reviews, and also the Feliks Audio amps as well as the Woo Audio ones. I’ve not heard them. There could well be plenty of others. I hope this helps!