The SNR is a measure of musical signal strengh relative to background noise. The higher the number in decibels, the cleaner the sound.
Speakers have efficiency/sensitivity and those with higher efficiency play louder given the same watts.
The amplifier and source will have a SNR. Keep in mind some companies use different standards for their SNR and some may not use Federal Trade standards for power output. So basically I wouldn't buy a product based purely on stats unless I knew what it meant.
If you use appropriate gauge wire, it will play little role in SNR. However the wires can be the cause of hum and noise. The interconnects, the different grounding or locations of components, and cables near strong AC fields can cause unwanted noise.
AMP big factor
speaker and wire little factor.