What aspects should I consider when designing a clean tube amp? ...
Start at the speaker/output-section, and design working back towards the input.
Bias of the output-section tells the drive signal required for max clean power output (any more just distorts the output-section).
Preamp + phase inverter gain = output-section bias - Peak Pickup Output.
Add a little extra gain for Volume & Tone controls that will make stuff more convenient.
One of the cleanest amps out there is a Standel 25L15.
Its preamp is 12AX7 --> 12AT7 --> 12AU7. Each stage is less-gain & more able to handle a large signal-input than the stage before. That means all throughout the preamp, the signal is unlikely to over-drive the stage that follows.
A triode can swing an Output Signal that is maybe 2/3 of supply volts.
We can understand the Input Signal size a triode can handle as Output Signal / Gain.
Say we have 300v supply, so at best 200v Output Signal.
12AX7 Gain =~ 60 ---> 200v Output Signal / 60 ---> 3.33v Input Signal
max before distortion
12AT7 Gain =~ 34 ---> 200v Output Signal / 34 ---> 5.88v Input Signal
max before distortion
12AU7 Gain =~ 14 ---> 200v Output Signal / 60 ---> 14.29v Input Signal
max before distortion
The lower-gain triode is therefore able to accept a larger input signal, apply a lesser Gain, and avoid bumping into some limit of operation (which would cause distortion).
Eventually, you will need to use load-lines to inspect how the tube is biased. If you bias any tube near Zero plate current, or near Zero volts grid-to-cathode, the tube will distort after only a small signal is applied. Biasing the tube halfway between these extremes will allow the tube to accept the largest input signal before distortion.
The 25L15's tone circuit also uses negative feedback for the frequency-control, so anything less than full-up is using some negative feedback which cleans up distortion.