If I learn Codeigniter, can I use it with Drupal or is that a bad idea and I should use Expression Engine?

Drupal & CodeIgniter are different PHP frameworks (Drupal could be considered the CMS that became a Framework). Your work/learning in CodeIgniter will undoubtedly give you perspective when working with Drupal and grow your coding skills, but it wont necessarily help you learn Drupal Core API's and Methodologies.

I recommend getting into Drupal cause it's hawt (in demand), once you get your head around assumptions & common patterns it helps you build things very fast, the community is huge and all the cool kids are doing it. But if you are learning CodeIgniter and want to leverage that learning in EE, that makes perfect sense...and if that's what you/your clients want, rock on.

To start with Drupal I recommend getting into what it can do out of the box with Core & Popular Contrib Modules:

http://drupal.org/documentation/structure

Here are a few more learning resources for drupal:

http://drupalize.me (video site with lotsa free content and fair priced paid content)
http://planet.drupal.org (the drupal planet feed, lotsa great tutorials come down the pipe)http://api.drupal.org (your friendly Core API docs)
http://drupal.org (excellent multisite search kicks butt for finding help on your topic)

Both Codeigniter and Drupal is great but Codeigniter and Drupal's structures are different. Learning Codeigniter for Drupal does not sound like a great idea.

Please don't use them both, cause you will just waste your time.Instead, start with CI cause it's easier, find out how the code works, develop some sites or applications and then start with Drupal which is much more complex at least for customizing, but yet more powerful CMS. I haven't tried Expression Engine yet, but it has really nice feedback especially from designers.