I'm not suggesting this is a good idea, but I'm tired of the linked list argument which kind of implies Rust is much harder than C for an equivalent linked list implementation. If you explicitly choose to lose the extra guarantees, Rust is about as easy as C to write a linked list in.
Working through the Entirely Too Many Linked Lists book in general is super helpful, since it deliberately runs into the cases that are hard.
Implementing a hash table in Rust would probably be fine as a toe dip too. It's that multiple-references-to-each-object part that really burns you in the doubly-linked list case.
These are probably the two best sites for small, exercise training programs in Rust. Once you've gotten through a few of them, you'd probably be ready to build something useful, which might be more interesting.