We’re keeping it simple with this one. Just a few basic elements to help you get started. As long as you know who your audience is, the message you wish to convey, and the information you need from the caller, the rest should fall into place quite nicely. Let’s face it, a voicemail greeting for a lumber company will probably be different than that of a psychologist’s office. One greeting is aimed at securing potential customers, and the other is geared towards appointments, more or less. Once you are certain who your caller is, the better your voicemail. Center on your audience, first and foremost. Knowing what to relate ensures that your caller will leave the right message. For instance, if you’re a retail store, you would include your hours of operations, and perhaps any specials that you’re running. If you are a therapist’s office, then you’d need to include an alternate number in case a patient is having an issue and requires immediate help. Again, this will vary depending on the business. Here, a therapist would definitely request the caller leave their contact information. However, a retail store chain might not request that. There are also complex voicemail systems such as those used by mobile phone services, which ask you to press a certain number on your phone, where you are asked to leave your account information. Again, as you can see, it all boils down to the demographics of your callers, and what you need from them to conduct the best business possible. Depending on the situation, your caller might be in a good mood or not. In either case, they’ll probably be eagerly awaiting your call. So, it stands to reason that you only promise them a call back if you can deliver. In other words, if you’re a small shop and you’ve decided to close due to a much-needed sabbatical, then don’t leave a voicemail greeting where you promise them to call right back. However, if you have an active customer service staff, then you can promise to return their call within the same day.
You'll notice that many of these are targeted, but cover things that can easily annoy users. Slow keyboard response in Quick Reply is one of our frustrations with iOS 9.1 that this fixes. Other upgrades fix alarm bugs, iCloud backup problems and much more.

At present, you have to record your greeting by recording directly into the iPhone microphone -- the results of which are average, of course.
Having a dedicated emergency contact will help make sure anything important that comes up is taken care of. Another option is directing callers to a separate answering service.