Next free value field I need a custom field whose default value will be a "next free" value calculated using a user-defined scope (selection of content types). But before I even try to bother coding, maybe someone knows of such a contributed module? My searches returned nothing.

I'd be reluctant to using Computed Field as I feel somewhat uncomfortable storing PHP code in database.
Perhaps you could just use a Serial field


  This module provides an auto-increment (serial) field.
  
  Unlike Drupal's built-in auto-increment node ID, which is global and
  shared by nodes belonging to all content types, serial fields are
  managed per content type (D6) / entity (D7). For example, the serial
  field of an Invoice instance will generate a unique sequential number
  (starting at 1, then 2, etc.) exclusively for Invoice instances.
  
  The allocation of serial numbers by this module is atomic. In other
  words, the serial values are unique even when multiple instances of
  the same content type / entity are created simultaneously.