Recursion looks scary but it is just a function that calls itself on a smaller piece, and the call stack does the bookkeeping. It is the natural tool for trees, the shape a document like a manual actually has.
The two simplest ways to decide what gets handled next: a queue (first in, first out) and a stack (last in, first out). Where each one shows up in real systems I have built, with examples.
The 'halve it every time' idea. How binary search finds something in a million items in about twenty steps, where it quietly powers databases and even git, and the one condition it needs.
The single most useful data structure I reach for: the hash map. What it is, why lookups are instant, where I use it in real systems, and the catches to know about. No jargon.