Which Editions of Oracle are Free?
Express Edition [XE] is available for usage by small businesses.  You get no upgrades or patches.  Support is only available by internet like Google and DBA SE.  You are limited to 1 CPU Core, 1 GB of RAM, and 11GB of user data.

Current version of XE is 11.2.0.2.  Version 18 XE is due out soon (October 2018).  I've read Oracle will then release newer versions on an annual basis.  Max user data is increased to 12GB of data.  But, "Adv. Compression" is suppose to be included (increases user data to est. 40GB).  This information comes from a post by the Project Manager for XE on the Oracle community forum for XE.

For personal learning, you can use any edition.

For your classes, I would probably use XE for the classroom but mention VirtualBox.  Oracle has a prebuilt VirtualBox VM for learning. A small list can be found here.

Additionally, http://LiveSQL.oracle.com provides a free "test stuff out" similar to "db fidle".  (I would not use that for classroom)

More details (with respect to licensing) should be referred to your local friendly Oracle sales representatives.