How should I configure mySQL 5.7 on Ubuntu for a physical Hot Backup? I recent upgraded my Ubuntu 14.04 server to Ubuntu 16.04. I managed to get mySQL upgraded to 5.7. I don't currently have anything in the mySQL instance. Since I have been an Oracle DBA for almost 20 years, I want to configure mySQL with some of the same features. I want to turn on logging for all transactions, and setup hot backups, hopefully using open source software. I'm also not sure which database engine to use.

I have been looking through the documentation, and I am just not finding the steps for setting up a mySQL instance to work they way I think it should work. I know I can do a logical backup, but that doesn't allow me to do point in time recovery. I know I can use all of the default settings, but if I am able to market my skills as a mySQL DBA, I want to use as many of the advanced features as possible.

Thanks.
Use Innodb unless you have a specific reason not to. If your coming from Oracle you will find its internal behaviour familiar therefore learning curve is shorter. 

For what you described you probably will want to enable binary logs (check which format suits your use case better: row, statement or mixed).

For hot backups I recommend to use percona-xtrabackup. It can stream data directly to a remote server so you don't even have to have double the free space available on the backup host. The documentation is very good and detailed and you can also find many source online. 

I hope this helps getting you started. Good luck!