What could I expect to hear from a Class A amp?

A lot depends on how the amp is designed. The supposed advantage of Class A operation is to eliminate crossover distortion. However, a well designed Class AB amp will not have appreciable crossover distortion. I doubt that reputable manufacturer designs class B amps

Bearotti: You may want to further your knowledge by looking at texts and articles from other than manufacturers of audio equipment. Those sources are generally biased to promote their product and do not provide a complete picture. Keep in mind that there is nothing particularly difficult in processing audio signals. Techniques that work in one area of signal processing work in other areas. For eg. in the mid 1990's I spent considerable time on a design project which applied signal processing ideas initially developed in radar target identification to extracting late potentials in ECG signals as an early predictor of cardiac problems.

Also keep in mind that in some 'perfect' sense there are tradeoffs in such things as class a vs class ab amps. However, those tradeoffs are meaningless because - as I indicate above - properly designed AB amps will not result in signal degradation that is in any way noticeable (unless of course one uses the magic 'audiophile ear').

A good beginning point for gaining more knowledge are the books by Douglas Self. These have very little mathematics in the explanation and are readily understood by anyone with a high school math background. The same goes for amateur radio publications. (Engineering texts and publications require a minimum of a formal course, or the equivalent, in differential equations and some background in Fourier analysis - which takes a considerable time investment - generally not a good investment unless one expects to make a living as an engineer)

It takes about 1 second of on time for a solid state amp to sound its best. The last piece of electronic equipment I saw that took any longer on time to sound its best was a tube television set from the 60's. (cannot speak for tube amps of today). Even that TV took only a few minutes to settle. Turning the amp on and off between listening sessions will not change the amp's lifespan in any meaningful way. Nor does an amplifier that is on but not driving a load use a great deal of energy so it shouldn't change your utility bill anymore than leaving a porch lite on 24-7. In short, these issues are of no more practical significance than the issue of how many angels can dance on the head of a pin.

Shadorne: Correct as to the unamplified nature of crossover distortion. It is only the ouput, or final, stage at which the bias point is placed near cutoff and saturation, respectively rather than centered - in a class B amp. How hard that stage is driven makes no difference as far as the amplitude of the crossover distortion since there is no amplification following that stage. But since the excursions will be greater away from the crossover point, when driven harder, any change at the crossover point (which will be insignificant anyway in an AB design) will be a smaller percentage of the overall signal. Hence, at low values of output signal any such distortion would be a larger percentage of the output signal. As to your comment regarding active speakers - absolutely true - it always makes sense to design the electronics for the load and the more known about that load allows for an easier design with less compromises.