I'd recommend writing something you might have used or be familiar with, in bare-metal C. Maybe try writing a simple web server, which is something most people will be familiar with. Try doing it a couple different ways: single-threaded, prefork (processes), event-based with select/kqueue/epoll. Write your own data structures: hash tables, linked lists, etc.

This sounds simple but will give you a good tour of a lot of different areas: BSD sockets, named pipes/unix domain sockets for cross-thread communication, signals, memory management, threading, basic scheduling, and parallel programming (locks/concurrency), to name a few.