You may prefer 600Hz (=48kHz/80) to 375Hz (=48kHz/128) for sidetone. If this is the case, you divide the interval [0, 2pi] into 80 sections rather than into 128.
Should I use a numerically controlled oscillator (NCO) so that only a single table is required for creating a signal with arbitrary frequency?
https://en.wikipedia.org/wiki/Direct_digital_synthesizer
I do not think so.
https://en.wikipedia.org/wiki/Numerically_controlled_oscillator
Phase jitter caused by truncating the phase accumulator output of N-bit into M-bit is avoidable in our situation, because only some particular frequencies, such as 607.6Hz (=48kHz/79), 600Hz (=48kHz/80), and 592.6Hz (=48kHz/81), are of our interest as far as sidetone is concerned.