All three work; the priority is rigidity and squareness, not the material. Aluminium V-slot/T-slot extrusion (2020/2040) is the popular choice: precise, easy to bolt up, easy to mount rails and motors, and it stays straight. Plywood/MDF is cheap and perfectly fine for a first build if you brace it well and keep it out of humidity. Steel is rigid and cheap if you can weld, but heavier and harder to modify.
For a foam cutter the loads are tiny — the wire barely resists — so flex from sloppy joints, not material strength, is what hurts accuracy. Whatever you pick, make the two towers identical and dead parallel.
For a foam cutter the loads are tiny — the wire barely resists — so flex from sloppy joints, not material strength, is what hurts accuracy. Whatever you pick, make the two towers identical and dead parallel.