You probably will find a lot more useful information on the AppHub site then these forums as your question is much more about XNA / 3D graphics then the math/geo/physics libraries found here.
My suggestion would be for you to check out the Chase Camera sample on the App Hub (formerly known as Creator's Club) website first.
Chase Camera Sample
If you go through the Ship and ChaseCamera class you should be able to get a sense of how they did it.
As far as avoiding LookAtMatrices etc there are certainly ways you could do that, however, to me, it seems that the LookAt Method of creating a View Matrix is the easiest and most straight forward.
To create movement in the direction of "Forward" you must first define Forward.
In the case of a third person game forward would be defined (generally, not always) by a vector that starts at the Camera's Current Position and Ends at the Player's current position.
Vector3 forwardDirection = CameraCurrentPosition - PlayerCurrentPosition;
which you would generally want to Normalize and then use as a direction to apply the motion in the direction of.
Hope that helps!