Educational practice problems/systems/reactions in computational chemistry
There's a free software quantum chemistry package called Psi4. If you're a GNU/Linux user, under Ubuntu or any Debian-based distro, you can install it with a simple terminal command.

sudo apt-get install psi4


They have a well documented site, including a section dedicated to education with simple projects and friendly message boards. As of today, they list the following projects in their education section:


What is the radius of an atom?
What makes a molecule polar or non-polar?
How do we calculate the most accurate energies for a boron atom?
Can we visually predict binding energies?
When does water become $\ce{OH + H}$? A study in molecular orbitals.
What happens to the orbitals as a one-dimensional box gets longer? A study in molecular orbitals.
Is $\ce{C3H+}$ present in the Horsehead nebula?
What is symmetry in chemistry?


The version available in Ubuntu repository is functional, but quite outdated, 1.1.5, as of Mar 2020. If one is serious about learning it, my advice is to download it directlly from their site. For me the only issue with it is that Avogadro, my output viewer of choice, seemingly doesn't provide native support to view Psi4 output files. But I count that as a missing feature in Avogadro, not Psi4.