MyBB Community Forums

I need to receive an email when a new user registers and when any messages are posted. What settings do I need to change? (I am the Admin)

You need a plugin for notification on new users, and I think you can subscribe to all your forums to get emails on new posts.

Unfortunately these aren't part of MyBB installation. For the email on register, I believe there's a plugin for that by Michael83. You can search for it on MyBB Mods http://mods.mybboard.net

For getting an email when any messages are posted, MyBB has forum and thread subscriptions, but you must actively subscribe to each of them (it's not possible to automatically get a notification without subscribing, unless you have a modification or plugin).