Scroll down to the “Greetings” section and click the speaker icon (manage) next to Voicemail Greeting. Click Add Greeting. Select the Record radio button. Enter the number or extension of the phone you wish to record the greeting on. Name the greeting. Click Call and follow the instructions given to you on the phone.
Even in today's fast-paced world, customers don't like being greeted with an automated message. According to the New York Times, callers of a certain age are put off entirely if they are answered by a voicemail instead of a real person.

Hi Deborah, thanks for reading! To delete a voicemail, open the Phone app and tap Voicemail. In the top right of your screen, tap Edit. Then, tap the bubble that appears next to each of your messages to select it. If you would like to delete all of your voicemail messages, tap every bubble until they’re each filled with a blue check mark icon.
People have short attention spans these days, and you should always craft your communications for the lowest common denominator with something as universal as your voicemail.