I'm not too familiar with Besta ( I have a custom made wall to wall display unit), thus I don't know if you can actually run the wires for the lights behind the cabinet without the use of a mirrored back to hide them. I can tell you I did hide the wires for my three Detolfs using Hide-A-Wire from Home Depot, and you cannot see them. I then connected those to a remote control module and I never have to turned the lights on manually. I could show you a picture later on if you are interested. Just let me know so I can look for it.
That said, the mirrored back is pretty much up to individual taste. Keep in mind that since it will reflect the mini busts and statues on your shelf, it will create the optical illusion of having more of them on it, thus giving the false appearance of being a little crowded depending on the amount you choose to display on each shelf. If you want a more simple, clean look, then displaying them without the mirrored back is the way to go, in my opinion. But again, you would need to find a way to hide the wires as I know how obtrusive they can be just hanging there. Personally I do not use mirrored backs, but that's just me. Whatever you choose to do, make sure it is the look you really want. After all you'll be the one looking at it every day. Enjoy your project!