I wouldn't recommend a $500 tube amp for the K-701. Reason being is that it has (IIRC) a 62 Ohm impedance.
Almost all inexpensive tube amps are OTL. OTL doesn't do well with lower impedance headphones, with just a few exceptions. The biggest one being the Zana Deux, but only because the 6C33C tube has exceptionally low output impedance. That's what makes it so special.
Most OTL amps will claim to drive lower impedance headphones, but you run into problems with the damping factor and excessive negative feedback to drive down impedance while also strangling (in my opinion) the sound. Further, I find the build quality of some inexpensive tube amps to be questionable. They cut all the corners just so they can sell the orange glow on the cheap.
The only way to get the output impedance nice and low short of a 6C33C (or a few others) is to use output transformers. Those generally aren't cheap. Not too long ago, I paid $500 to have a pair of Sowters shipped over from England. That's just the output transformers, not anything else in the amp. A good pair of output transformers will start around $200 and they just go up from there.
If you have to have an amp that glows, look at some of the hybrids. Those can have an acceptably low output impedance while still giving some tube flavor.
But if I were to keep it under $500, I'd go with a quality solid state amp. Solid state doesn't require a high voltage power supply, so you can get good quality at lower prices. Though tubes are all the rage (and I run lots of them), solid state offers great quality for the price. I think a lot of solid state amps sound terrific and wouldn't be
that upset if rhey were all I had.
A Gilmore Lite, EC/SS, M^3, CK2III, or a Beta22 would be easy to live with.
