If I was going to make a FPS camera class it would look something like yours but with a different internal representation of the look vector as spherical coordinates. This makes the logic for mouse-look much easier to understand and requires a simple spherical-to-Cartesian coordinate transformation whenever you construct the View matrix


// Camera.h
struct Camera
{
D3DXVECTOR3 Position;
float RotX;
float RotY;

D3DXMATRIX View;
D3DXMATRIX Proj;

Camera(D3DXVECTOR3& position, float fov, float aspect);
void Update();
};



// Camera.cpp
Camera::Camera(D3DXVECTOR3& position, float fov, float aspect)
{
Position = position;
RotX = 0;
RotY = 0;
D3DXMatrixPerspectiveFovLH(&Proj, fov, aspect, 0, 100);
}
void Camera::Update()
{
POINT mousePos;
GetCursorPos(&mousePos);
SetCursorPos(640, 480);
RotX += (float)(mousePos.y - 480) / 500.f;
RotY += (float)(mousePos.x - 640) / 500.f;
// change 500.f to any value to adjust sensitivity
// change += to -= if it rotates the wrong way
D3DXVECTOR3 look = D3DXVECTOR3(cosf(RotY) * sinf(RotX), cosf(RotX), sinf(RotY) * sinf(RotX));
D3DXVECTOR3 target = Position + look;
D3DXVECTOR3 up = D3DXVECTOR3(0, 1, 0);
D3DXMatrixLookAtLH(&View, &Position, &target, &up);
}


First, did the code work as you want?

http://en.wikipedia.org/wiki/Spherical_coordinates

Basically, instead of storing a vector that tells me the direction the camera is looking, I store two angles - one is the "up/down" angle and the other is the "left/right" angle. In a spherical coordinate system, there is a third number - r, the distance from the origin - but that is always 1 in this case so I leave it out.

The advantage of storing the angles rather than the vector are that it is very easy to adjust the up/down/left/right angles through which the camera is looking - as you can see, I use the mouse like most FPS games do.

Now, to build the View matrix I need to pass in a target vector, described by the camera position + look vector, so I need to calculate the look vector from the spherical coordinates (RotX, RotY, 1). That line of code gives the look vector in terms of RotX and RotY (multiplied by r = 1)