From what I can recall, biverting improves contrast because the inverter chip matches the positive and negative voltages at a much higher accuracy than the DMG can. In layman's terms, the inverter does a better job at matching colors(or shades, rather) than the GameBoy.

Most of the backlights you'll see operate in very similar fashions. The big difference you'll notice is how noticeable things like the LEDs at the bottom are. I've heard good things about Kitsch-bent, as well as Nonfinite(although I've also heard negative reviews about him). I purchased my backlight on Hand Held Legend and it works very well: http://handheldlegend.com/collections/p … and-pocket
If you think you're up to it, I'd recommend also installing a bivert mod, but it isn't necessary and you'll still get a pretty good picture just from having a backlight. Correct me if I am wrong, but I believe that there isn't any difference in the functionality of the different backlights for sale, they're just constructed a little differently. If you're new to modding, I would recommend buying a kit from HHL or Nonfinite that has the backlight, as the KB lights are a bit more advanced(e.g. the RGB allows for color change). If you still haven't figured out a kit by the time you look at the options from the aforementioned vendors, I would suggest looking at some online reviews, and decide based on the one that looks best to you. I personally prefer the HHL backlight, as it's a bit thinner(so it's easy to fit) and comes with the wires and resistor needed. If you want a guide on installing, I would recommend the videos by This Does Not Compute and Nonfinite: https://www.youtube.com/channel/UCEp20N … dbQdHSxgjw https://www.youtube.com/channel/UCqWPeY … vnO1fwRSHw