Which Salesforce Edition should I sign up for to learn how it works?

Follow the below link to learn. Below is the developer org and you can access every new feature...

https://developer.salesforce.com/signup

Also refer TrailHead and complete all the courses. Use the same signup credentials

https://developer.salesforce.com/trailhead/en

For your use case you need Developer Edition. Just go to Developer edition and signup for a free account.

Also take a look at Trailhead and some developer module which help you get started.

Sign up for a free developer org

https://developer.salesforce.com/signup

Developer Edition (often referred to as a "DE org") is a fully-featured development environment with limits on data and users.

When you're ready to begin developing, you'll find that Developer Edition is equipped the full Salesforce CRM suite, along with all the latest developer technologies. Sign up for a Developer Edition and you'll get your new environment provisioned immediately. Note that Developer Edition orgs continue to be available as long as they have some type of activity within the previous six months.