What do people recommend for bringing this line to the back of your
fridge in the wall.

I want something i dont have to worry about.

I notice my home store sells kits in both copper tubing (flexible) for
bringing water for auto ice makers etc and they sell another kit or
line that is braided steel (or simular) over flexible pvc.

The package on this one claims there is nothing stronger.

I dont know. I want to do it right and not have to worry about it
leaking or bursting.

Any recommendations?

Thanks!