What is the appropriate way to store arrays of information with configuration API?
You define a schema type sequence:

Example: /core/modules/options/config/schema/options.schema.yml

# Schema for the configuration files of the Options module.

field.storage_settings.list_integer:
  type: mapping
  label: 'List (integer) settings'
  mapping:
    allowed_values:
      type: sequence
      label: 'Allowed values list'
      sequence:
        type: mapping
        label: 'Allowed value with label'
        mapping:
          value:
            type: integer
            label: 'Value'
          label:
            type: label
            label: 'Label'


You'll find the form for this example in /core/modules/options/src/Plugin/Field/FieldType/ListItemBase.php

More info https://www.drupal.org/docs/8/api/configuration-api/configuration-schemametadata