What is the best way within QGIS to select all of the features within a rectangular bounding box? Is it necessary to create a separate layer with the box, then to use the intersection tool within vector research -> select by location?
Obviously you can do rectangular bounding box selection with default selection tool with mouse/touchpad down + hold and move + up (there is also selection tool by polygon, freehand and elipse)
You can also use Select features using expression and make selection by comparing feature Geometry xmin, xmax, ymin, ymax to your extent - minimum, maximum coordinates.
And yes, there is also tool you already mentioned - Vector - Research Tools - Select by location...
All depends what you want to achieve.