make "z" toggle between textured mode and wireframe? Is it possible to make the keyboard button toggle between wireframe and textured 
instead of wireframe and solid?
It sure is. Just go to Blender's preferences in the Input tab. Search by key-binding: "z". In the 3D View section you will find three "Context Toggle Values" shortcuts, one being assigned to the z key only (no modifier keys). Expand this and change the value of "SOLID" to "TEXTURED".



There is a small yet notable inconsistency in labeling that, in the UI it is listed as "Texture" yet its value name is "TEXTURED" with a D on the end.