Which SQL Server Express edition is right for me?
Backup are automated via SQL Agent jobs in SQL Server.  Since no express edition includes the SQL Server Agent, then you would have to find a way to have your application initiate the backups. Otherwise, you need standard edition.  

What other features are you using?  Some of them may require enterprise or standard.  Personally when I was doing a lot of development, I would try to use an edition that matched what an average target user would have.  So If I want them to have SQL Express, then that is what I used for my development.