I think it’s best to consider technical specs to be an indicator of the quality of the item rather than how it will sound. Harmonic distortion describes how linear the amplifier is (how closely the output resembles the input) which is important, however the difference between 0.001 and 0.0001% is unlikely to be heard... but it is an indicator of the quality of the overall design. The method of measuring THD uses a simple sine wave as input which causes some to say that it’s not representative of music. Intermodulation distortion measures the reproduction of multiple frequencies and so is often considered to be a more relevant spec.
Noise measurements are pretty indisputable (THD+N, Noise Floor, Signal to Noise Ratio). The greater the SNR the less noise there will be, but again, the difference between 115dB and 120dB is unlikely to be audible.
In general, if you know how to read them then graphs are much more informative than numeric values (0.1%, 100dB etc.).
In terms of putting a system together the least used tech specs (in my experience) are the most important ones... gain (or output level), impedance, power and loudspeaker sensitivity. They don’t tell you how good a component is but they do tell you whether it will play nicely with the rest of your equipment.
One last point... if you’re comparing different specs be sure to read the small print e.g. the conditions measured. Was THD measured at 1W or full output power, was loudspeaker sensitivity measured with a 1W or 2.83V signal, these things matter. Also if you’re trying to compare a % measurement with decibels there are plenty of online tools that will convert between the two.
I think the problem with specifications is that you need to understand what they’re telling you to make use of them and that takes a bit of effort to learn.
Nothing beats listening as long as you get a decent amount of time to figure out whether you like how something sounds.
