Generally speaking, a amplifier should deliver stable voltage across the entire frequency range without any bumps to any specific ranges, so in reality, amplifiers should be bought based upon quality. PERIOD.
Speakers, on the other hand, can have all sorts of sound characteristics that run the gamut and in any specific room a set of speakers that may sound great, could sound terrible in a different space. So, it is important to buy speakers for the room you are putting them in. That's the first, and most important step.
From there, you can buy an amp which is of high quality and if you buy 12 different amps, of high quality, you should be completely incapable of hearing the difference between any of them. Of course, if you are playing audio at the same volume and within the power capabilities of the amplifier in use. An underpowered amp for your speakers will be underpowered forever. So, get enough power.
At the end of the day, we have some members which can be a bit harsh on the subject, but really, there are 'bad' amps out there which may not sound good and don't deliver across the frequency spectrum as they should, which could impact sound. Yet, from major manufacturers of quality product that is well recognized, it is not a common occurrence.
IMO - It is better to just ask about the amps you are looking at and the speakers you are getting them for, then read the responses you get.
But, get speakers for a room, then quality amps (or an AV receiver) to power them.