Do Not Disturb is a good idea, and then either arrange for Contact Favorites or Select Contact Groups or lists of specific users.
Settings -> Notifications -> Do Not Disturb -> Allow Calls From
Another approach is to find a "Silent" ringtone (Google). Install the Silent ringtone and set it as your default. Also set a no vibration as the default. Now for each contact where you want to phone to ring, you can give them an explicit ringtone and vibration.
The Do Not Disturb would most likely be easier to configure and maintain, but I figured I would offer the Silent ringtone option as well.