With a vinyl-linered pool, which walls are best: steel, aluminum, resin, or concrete?

Steel is strong, but it can rust.  Aluminum does not rust, but it’s weaker, and it does oxidize somewhat in alkaline soil.  Resin does not rust or oxidize.  It makes curves precisely, but it can crack.  Concrete is by far the strongest, but it’s rough, it cracks, and it does not allow for as wide a variety of interesting shapes.  Plus, the wall material is not as important as the construction techniques.  The wall really doesn’t do that much: mostly it keeps the liner uniform and holds back the dirt.  Once you get down to the bottom, in fact, the pool really is just dirt with a covering to protect the liner.

A good construction technique will tie the wall together with a lot of concrete; either all the way around, or at the stakes that hold the panels in place.  If you are going to have part or all of a wall above the ground, a solid concrete wall would probably be best: say ten or twelve inches thick, like a house foundation.

I’d be more inclined to choose a builder who I thought would do a good job, and use the wall and construction technique that the builder recommended.