What materials are suitable for making a mini gas turbine engine?
Materials are one thing. You also need tools and machinery to build one: the turbine and compressor in a mini jet engine rotate at ~100,000 rpm so they're subject to significant stress. They have to be balanced perfectly. 

If you want to build one yourself, look into using a turbocharger from a car engine as the core. That gives a decent base for the high-temperature parts of the engine. Others have built DIY jet engines from turbochargers.