I generally prefer a fairly smooth sound. However it actually helps to have some string noise in the mix.
I address excess string noise in two ways:
1. I have a light touch and fairly clean technique (reduce the source).
2. I dip high mids (correct).
IMHO clank exists mostly in the frequencies around 3K or so. So a gentle dip in that range will reduce clank. It helpful to have a parametric to dial in the best center frequency and bandwidth.
I like glass and air, which are encoded in the frequencies above clank. So I don't typically dip the treble.
Some of my older Mesas are stubbornly resistant to using EQ to mitigate string noise. I think they generate distortion in the high mids, as in some instances turning down the gain seems to help.
One of my favorite tubes to roll into bass amps is a current production Mullard ECC83. IMHO in many of my amps, this tube seems to smooth out the high mids and also extend and tighten the lows. Sovtek 12AX7PS sounds very similar in the mids and highs, but is looser/more wooly down low.