(1) To add specific tools inside a tool section:
Right-click on any tool section (like the 'Page Navigation' or 'Page Display' tools) of your toolbar.
And select the specific tool you want (a checkmark next to the tool will tell you which ones are currently selected).
(2) Customizing other toolbars
Try right-clicking on the toolbar and exploring other options to add to the main toolbar.
Word of caution: Acrobat doesn’t show checkmarks next to the tools sections that are currently showing (nor dim them nor provide any other sort of visual feedback).
So it’s not immediately clear, for example, that when a tool has been added to the toolbar, right-clicking and selecting that tool again from the dropdown menu will remove it from the toolbar but leave the other ones you added alone.
If in trouble, just choose 'Reset Toolbars' and begin again from scratch.