Looking for a way to limit access to nodes of a content type by role

I have looked at the various node access modules and know that it is possible to limit access to individual nodes by role. However, I would like to:

1. Limit access to content types.
2. Have this access limited by role, not by user.
3. Automatically redirect when a user without permissions tries to access a content type the don't have permissions to access.

Is this possible? What modules or combination of modules do I need to do this?