On the iPhone, go into voicemail and tap "Greeting". Record a few seconds of something and tap stop. Before you tap save, use iFuntastic or SFTP to navigate to /var/root/Library/Voicemail on your iPhone. You'll see a file called "Greeting. amr". This is the audio you just recorded. Delete that file and replace it with your custom message which should then be renamed to "Greeting.amr". Tap "Play" on the iPhone to verify your message works. If it plays, tap "Save" and your custom message will be uploaded to AT&T's servers.
Yes, you can be charged. This depends on the service. For example, Spectrum’s Voice Residential Services Price Guide charges $3.95 for voicemail.

A professional voicemail greeting is a recorded message that welcomes callers to your business when no one is available to pick up the call. For a polished call experience, the greeting should reflect who the client is calling – whether a general business number, department, team, or individual – and when the customer can expect the call to be returned.
Hello, you have reached the dental office of Dr. X. We are busy assisting a patient now, but will call you back as soon as possible. Please leave your name, reason for calling, and your number. If this is an urgent enquiry, please call 911. In this case, the dentist is giving a reason for not being available and they’re providing a way to prioritize the patients who need the most help. They’re also leaving an emergency number for the most severe of situations.