How can I set up a two part sign up form, where first submit leads to second with more fields?
To implement this purely in CiviCRM with WordPress:


Create a standalone profile form to collect name, email, etc.
Create a second profile form to collect other information. If you want it to record an activity, you can set it up as a "Petition" form. If you want it to register the contact for an event, embed it in an event registration page.
Back to the first profile, edit and click the "Advanced Settings" tab at the bottom - set the "redirect url" to the public url of the second form.
Create a page or post in WP, and click the CiviCRM button to insert a shortcode for the first form.


Note that users must be logged in for Civi to already know who they are on the 2nd form. You have 2 options with this:


Users are already logged-in prior to filling the 1st form
On the 1st form, (also under "Advanced Settings") you can have Civi create a user account for them.