Reddit reviews Gas Turbine Engines for Model Aircraft

Get this book. There you'll learn how hobbyists do it. That book has full plans and instructions on how to build a working jet engine from scratch.

And, to answer your question, at that scale a centrifugal compressor is better.

It's not very useful, as it's too heavy to use in a model aircraft.

A small and lightweight gas turbine could be built using the tools and ability this guy has, the full plans and instructions are in this book