I’ve encountered a few ski binding collectors over the years. Generally, the theme is the same. You make some kind of “board” you mount the binding on, then hang on your wall. I’ve seen collections installed on sections cut from discarded skis (funky, but too busy for my taste). Others live on fancy boards that took master woodworking skills to create. My approach is to use simple 1×4 inch planks with the edges slightly eased. The wood is affordable clear poplar that holds screws slightly better than pine and comes quite straight. I try to mount the bindings in consistent fashion so the toe units, at least within in a brand, line up horizontally. If the ski touring binding has a brake that doesn’t stow I either tie it up with a strap, or place screws on either side of the plank to act as hooks for the brake arms.
Our museum room (otherwise known as our house entryway, hah) is done in North American “drywall sheetrock” style, thus simple drywall screw anchors with a protruding screw work well for hanging. Downside with screw anchors is they leave blemishes if they’re ever sunk or removed. That’s not a problem for me because I have a home improvement skillset that could populate a one-man reality show — including my secret drywall talents. But if you’re concerned about gouging your sheetrock you could use picture hangers that leave tiny nail holes; easy to fill and hide during a repaint.