What is the right way to maintain a "version for the server" - with only config files changed, in Git?

You could keep versioned:

• two "value config files", with the right values for each environment
• a template config file, with value placeholder in it (for instance, @@PORT_NUMBER@@)
• a script able to generate the actual config file depending on the current environment
• a content filter driver which, on checkout, will trigger the script in order to generate the right config file.

Note: that supposes your template config file has a recognizable content (the filter doesn't have a name or path of the file). See "Git equivalent of subversion's $URL$ keyword expansion" for more on the limitation of git content filter driver).

It depends on Your needs. In my company we use other approach. We've created several environments (where the asterix is internal project name):

• devel - site runs on domain **.local.com*
• test - site run on domain test.*.company.com
• beta - beta.*.company.com
• production - every other domain.

Based on the domain name we switch automatically configurations. Basicly config file looks like:

<?php
return array(
  '_env' => array(
    'devel' => array(
      // config for devel
    ),
    'production' => array(
      // config for production
    )
  )
);
?>

Some frameworks (AFAIR Zend) set the environment name in Virtual Host config (or .htaccess). You should look at: zend framework auto switch production staging test .. etc

Have You looked at CI documentation? There's a section about it.