Components of 'entertainment' audio systems are often specified in very confusing and dishonest ways, so you have to use a lot of cunning in interpreting what is claimed for these products. I am an electrical engineer, so I can help you to some extent.
Firstly, when 'RMS power' is quoted, this, to an engineer, is nonsense, since the product of RMS voltage, and RMS current is 'average power'.
When an amplifier (or other component) is driven at full power with a constant sinusoidal signal, the maximum average power (averaged over a cycle) which can be used with safety and without excessive distortion is often quoted as the 'RMS' power.
However, the power delivered by a sinusoidal signal varies with time during the different phases of the waveform, and at the time of peak voltage (the crest of the sinusoid) the peak power is twice the average value. Since this is larger than the average power, and looks more impressive on paper, the 'peak power' of an amplifier is sometimes used in its specification.
With a loudspeaker, the situation is different. The main limitation to power handling is over-heating of the voice-coil. The average power rating with a sinusoidal signal (so-say RMS power) could be interpreted as meaning the maximum continuous average power which will not damage the coil by overheating. The peak power rating would then be the power in a short-term peak of signal (the duration should be specified) which could be handled without the speaker tearing itself apart mechanically, or blowing its coil like a fuse.
With these ideas in mind, an amplifier with average-power rating ('RMS') of 50W per channel would be capable of reaching the maximum specified average power rating of the speakers, but could not exceed it (I am not certain how to interpret the 8W part of the speaker specification). This would be a safe option. The amplifier would be incapable, even when working continuously at full output, of damaging the speakers.
On the other hand, since music is by its nature very 'peaky' (meaning that the loud parts are infrequent, most of the music being a good bit quieter than the transient crashes of cymbals or beats of a drum), you might consider using an amplifier capable of something near the peak capability of the speakers (250W), on the basis that the average power might be within the 50W limit, when averaged over a few seconds, and the amplifier could not exceed the peak capability of the speakers. This would be a more dangerous choice, since if you accidentally caused a continuous hum at 250W you would almost certainly damage the speakers.
So an amplifier rated between 50 and 250W would be suitable. How far you go towards 250W in the search for deafening power would be up to you, and how expensive replacing the speakers might be, should you have an accident.
