Best bang for your buck light.
 

When people ask about an affordable good quality HD shotgun almost every answer comes back mossberg 500 or Remington 870.

What s a good affordable light system for those guns?

I'm a big fan of the sunwayman products. Maybe a tad pricey but well worth the money.
http://www.sunwayman.com/html/products/201112/69.html

Check out Surefire G2X and 6P with LEDs.

For other budget lights check out Fenix lights and 4Sevens lights.

Streamlight weapon lights are good too.