Speakers do not have any power - hence do not have a power rating. The quoted wattage figure is a nominal power handling figure.
Amplifiers have a power rating, typically quoted as an RMS figure, standing for root mean square. Sound waves (generated by an amplifier in terms of current) go up and down, so measuring these peaks and troughs meaningfully becomes difficult, hence taking an RMS approach, think of it as about 0.6 of peak or so, hence a 6W amplifier might actually produce 10W when run hard.
Clipping is what damages or 'blows' speakers. If the volume is turned so high that the amplifier cannot reproduce the required current peak then a prolonged 'flat top' peak is generated. Speakers react to peaks by vibrating - a peak will push a speaker driver outwards. A clipped signal asks the speaker cone to travel outwards and not return, something speakers don't like - hence damaging it. Think of it like taking a slap or a prolonged hard press against a cheek...
Given the above it should be clear that a higher rated (or bigger) amplifier is far less likely to damage speakers than a smaller one as it has more head room to produce accurate peaks without clipping.
In any case, just don't turn volume controls up beyond distortion levels and all should stay well.
Regarding your choice of system and budget, that money, if spent wisely and with some patience, will yield a little used separate amplifier and (say) tuner which will be night and day difference in sound quality. I have a really good tuner spare you can have for free for starters.