I need to store an array of integers for configuration of a custom module - which of these is right? This is a list that is permanently recorded that should be able to change at a later time, either adding or removing items from the array at a user's discretion.

First method:

variable_set('module_listOfIntegers', serialize($arrayOfInts));


Second method:

$serialized = serialize($arrayOfInts);

$num_updated = db_update('module_config')
-&gt;fields(array(
  'listOfIntegers' =&gt; $serialized,
))
-&gt;condition('config_name', 'config_name, '==')
-&gt;execute();


And the final method could be creating a 2nd table with a single column where each row just holds the integer.  That seems a bit excessive for a simple array, though.
For saving module config settings, I use variable_set() in conjunction with the system_settings_form() function. Just also note that it and its companion variable_get() do the serialize/unserialize for you, so, there is no need for you to be doing it.