I have two types of users on my site:
How do I set up Drupal so that you can choose which type of user you want to be before signing up, and then also (and this is the tricky part) give different profile fields to the different user types?
Consider the Auto Assign Role module. Here is a quote about it (from the module's project page):
... serves three primary purposes. The first is to provide an automatic assignment of roles when a new account is created. The second is to allow the end user the option of choosing their own role or roles when they create their account. The third is to provide paths that will trigger a specific role when an account is created. The administrator has full control over these functions and can have them working together or independently of each other. Auto Assign Role is integrated with the Content Profile module so that you can have content types serving as registration pages. You can even replace the default user/register page with a customized version of your own design.