Can you suggest (and more to the point link to) Android apps with similar functionality to Voicemail Lite (or other voicemail apps) in the Play Store?
I personally haven't used Voicemail Lite, however I use Google Voice and like it a lot. I can get email notifications when I miss a call or get a voicemail. It also has voice to text capabilities so you can read your messages, rather than listen to them. Of course, you can listen to them as well. In addition, you can screen incoming calls, but choosing to either answer them or send them to voicemail. If you send them to voicemail and they leave a message, you can listen to their message as they're leaving it and press a key to come back into the call if you end up wanting to talk to them at that time.
Let me know if this helps!