Hi
@epaulino26. I can strongly recommend Viva. A few thoughts... Viva's house sound is the polar opposite of warm or rolled off or euphonic, at least not in the traditional, older tube amp sense. All Viva products, regardless of the model or the tubes used, are tuned to be neutral and highly transparent. The holography, clarity, realism is mind blowing. They represent the best of the "modern tube amp" sound imho.
With that out of the way, the Classico may be a great option, particularly if you want to also use it in a speaker system (I am running a Viva preamp in my speaker system). I know some Viva dealers recommend the Solista/Solistino/Classico for headphone use (with adapters) as well. If you end up deciding to go for a dedicated Egoista headphone amp from Viva, please take the opportunity to demo, preferably both the 845 version and the 2A3 version. They have different sound signatures, but both are state of the art.
You might have already read this comparison, but if not, it may prove to be helpful in your search:
https://www.head-fi.org/showcase/viva-egoista-amplifier.20334/
For the converter box you referenced, I've never heard of it.