I would use a quality solid state amp, like the Gilmore Lite, M^3 or EC/SS. Most of the inexpensive tube amps have cheapened power supplies to save money. Nothing is more important than the power supply in a tube amp.
I know tuberolling gets the majority of attention with tubes, but the power supply is the biggest factor in determining quality. You essentially are listening to the power supply, so its quality is of the utmost importance. If you have a little AC ripple or other nasties coming through, then the HD-800 will hold those up for you to hear. It is an unforgiving headphone. The problem with tube amps is that building a good power supply costs money. Good filtering, regulation, chokes, etc. add significantly to the cost. So unless you are prepared to buy an amp that has a great power supply, then you will not get the full benefit of the HD-800.
Solid state, on the other hand, is relatively inexpensive to build a power supply for. Chips run on far less power so you don't have to use big iron to smooth the power. Much less expensive options are implemented.
So go with a quality solid state amp and save up for a good tube amp. Or build your own, which is the least expensive option.