For the particular display you show, you would want option 3 for
define('CAT_BOX_ACTIVE_LEVEL', 'active|highest_level|deepest_level');

3=full active tree, others limited per level controls
and
The "highest_level" field controls whether top categories will display: 0=all levels/1=no topcats/etc.
The "deepest_level" field controls whether subcategories will display: 1=only first subcats/2=first & second subcats/.../9=all levels down to 9.