Leo says there's an app called Pushbullet that will deliver phone notifications to his computer through the web. Ryan needs something that direct his voicemails to his email, though. He has tried Google Voice, and that works for voicemail but not necessarily text messages, because those would default to iMessages on his iPhone. If he can get people to text him to his Google Voice number, then he can check those texts on the web.
Since Ryan's phone provider is AT&T, he can use AT&T's web-based interface to check his calls and messages. It's called AT&T Voicemail Viewer, and he can find out how to get it at http://www.att.com/esupport/vmviewer/.