Can I choose what is saved to my PS4 Backup file?

Yes, but your choices are limited. Captures, saved data, and settings are backed up by default. You can choose whether or not you would like to save applications (this includes games), but you can not specify which ones. You either need to elect to save all applications, or none at all.

If you would like to make a back up of the system with only certain games/applications, you will need to remove all others from the internal hard drive before creating the backup.