Though I don't listen to classical, I do listen to acoustic guitar and vocals.
It never sounds what I would call "harsh" but it can be a little edgy for some tastes. Of course, a lot depends on table, arm, phono and cable.
Also, classical is a very broad genre, piano solo is one thing and full orchestra another.
If going with Nagaoka I would go with top of the line MP500. Another possible option is Audio Note MM, more expensive, I think. I have not heard it. But after the table upgrade not before it. In my view, you start with a very good table and go from there. Besides, table can last for decades if you take care of it, and it does not require a lot of care.
When I bought my Nottingham Spacedeck/Spacearm lightly used for $1350, it was very expensive to me but I am glad I did buy it.