How do I create custom content types in drupal? I need to create a content type that is similar to a textarea, but I need to do some server side formatting before it can go out to the page.

I want a user to be able to input a chunk of text, then if it's a link of a certain type, leave it be, if it's not a link, create a link of sorts out of it with some server side (PHP) magic.

Can this be done in Drupal? Can someone point me in the right direction?
Yes this can be done.

For the processing you'll need a custom module. Here's a tutorial to get you started with modules.

As for the specific functions you'll need all revolve around hook_nodeapi (d6) or node api hooks (d7).