If I worked half of 2019 as an independent contractor and half as an employee (for a different company), what edition should I file under? Deluxe or Self-Employed?

You can enter Self Employment Income into Online Deluxe or Premier but if you have any expenses you will have to upgrade to the Self Employed version.

How to enter income from Self Employment

https://ttlc.intuit.com/community/self-employed/help/how-do-i-report-income-from-self-employment/00/26653

Thank you.