I'd also recommend the HD-600 over the DT880. I had both and slightly preferred the HD-600, too. Though I like the DT880 and recommend it.
One wonderful thing about the HD-600 is that it is available used for $200 or so. That might be the best deal on the market for an excellent headphone. Headphones are the most important part of the chain except for the recording itself.
Next, I'd look for a suitable amp. Do not buy a combo DAC/amp. The reason is that a good amp is a good amp, and the technology doesn't change that much. A great headphone amp from ten years ago still is.
DACs come out with new chipsets constantly. If you have a good amp connected to an older DAC, people won't buy it. More a matter of fashion, since I don't think a DAC makes much difference. But that's how the marketplace works and you don't want to be stuck with something others won't buy or expect a huge discount on.
There are three good amps to consider. One is a new version of the classic Dynalo available for $300. It has been around a long time, a Gilmore design, no caps in the signal path, over 1W of power, clean, crisp, and neutral. Lots of people have built a DIY version (me, too) and the only criticism you'll find is thst it's "old." Yeah, but it's done right and is a better circuit than a lot of new ones.
Another great amp is the Bottlehead Crack. About $220 and $300 with the Speedball upgrade. It's a kit, but an easy build and tons of support. You can run tubes and an OTL is fine for a HD-600. Many people have built it and it's a solid amp. I loved the one I heard at CanJam.
You might want to consider the new O2. About $100 to build, though you'll have to do more work than a Crack. Still, it could be a good option.
As for a DAC, just get a used one off Audiogon for $100 or so. You can always get another and it doesn't matter that much anyway. If you're not getting static, noises, dropouts, etc., then it's about as good as it's going to get.
That leaves a bit of a budget to go.
I'd take what's left and pick up a used Rega P3/Planar 3 for $400-$500 on Audiogon.
OK, you'll go over budget to set up the deck, but it's not bad. $50-$70 will get you a nice Shure or Grado cartridge, $100 for the very good NAD PP2 phonostage, $20 for the Shure scale, and $5 for a level. But you
might be able to pull it off under $1,000 if you go with a Crack or O2. That would be well worth the soldering.
So you could end up with one of the best headphones on the market, all the music on your computer, a solid tube amp, and a very good turntable with one of the best arms made.
I think you'd be quite happy with that.
(Not to lead you into temptation, but another $1,000, spent correctly, could add an excellent speaker setup to this rig.
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