I've used steel, galvanized steel, stainless steel, brass, aluminum, oak, maple, etc.
Most of the time I use brass shims because they are easy to find, can be easily cut, holes punched, and not too expensive. I usually buy a variety pack, currently the ones I have are a six pack sampler 2" x 6" item 27k0750 from Lee Valley Tools $8.95
For thicker shims I really like aluminum because it is so easy to work with and uniform in thickness
Drilling brass shims use a brad point bit, sandwich the shim between to pieces of wood/plastic etc. or if you have them a bullet point bit. Thin stock can easily be punched with a leather punch
Hardwood has been used for centuries because of their resistance to wear on heavy machinery
I don't think it matters, just use what is convenient; once bolted they all will remain stable
NOTE: when using wood it needs to be acclimated to your climate then seal it with a water resistant coating [oils/grease/acrylic lacquer etc.]
You will get old if you live long enough!