The wire will always be copper magnet wire. The core material will vary with frequency. What kind of radio do you have in mind? Is this a first project?
By the way, those inductors are wound on a cardboard form and have a ferrite slug inside to do the tuning. L2 is center tapped.
The schematic has some age to it. You might want to look further, as several semiconductors may be hard to find, like the double gated JFET. Superregenerative radios can be a bit of a trial, as they as they are so sensitive to layout and technique.