NANDulator is a simple, lo-fi, CMOS-based noisemaker synth. It uses two IC's, a CD4093 (quad NAND gate) and a CD4046 (VCO/phase-locked loop), and a handful of passive components. I think it's simple enough to work as a beginner's project, and there's also room for modification/hacking.

More info and schematic available from the FSA website:

https://www.fstateaudio.com/?page_id=1567