If you’re ready to go the professional direction, congratulations! Here are some websites you can use to hire a service to record your greeting.
At present, you have to record your greeting by recording directly into the iPhone microphone -- the results of which are average, of course.

There is no option under this to change voicemail greeting. When I go to My account settings there is only the option to forward calls or to go to voicemail but no option there to change the greeting (as the on-line versions show). I receive voice-mails and can retrieve them so I have this feature. Thank you! This thread is locked. You can follow the question or vote as helpful, but you cannot reply to this thread. Subscribe Subscribe Subscribe to RSS feed Report abuse Type of abuse Harassment or threats Inappropriate/Adult content Nudity Profanity Software piracy SPAM/Advertising Virus/Spyware/Malware danger Other Term of Use or Code of Conduct violation Child exploitation or abuse 250 characters remaining Cancel Submit Replies (71)  Microsoft Agent Moderator
Funny Voice Mail Greetings - Phone Message Downloads The following audio collection contains funny, bizarre, and sometimes down right strange greetings that will be a sure fire hit with your caller. Expect lots of laughs when you add these hilarious and unusual answering ringtone audio messages to personalize your mobile and home phone.