Kyrill,
In my experience, the quality of the socket makes very little sonic difference, though the resistivity of the material, particularly around the grid termination, is important.
The choice of tube is important, with many reporting the highly expensive gold pin Siemens 7308 amongst the best. But the 6ES8/CV5331 is variable mu and slightly more euphonic. It does depend on whether you want the organic sound or the ultra clean sound; preferences do vary.
As for damping, I'd suggest a springly plastic damper or Pearl tube cooler as these work directly on the glass envelope, just where you want it......
Hope this helps,
Hugh