I have a really hard time trying to point the camera by
rotations and positioning it through top and side views.
I can’t seem to guess which combinations of tilts and rotations
will get me pointed at the model.
Is there anyway I can use the camera window and a set
of keys to dolly, pan, tilt and dutch the camera without having
to resort to mousing the camera around on a 2-D projection?
Yes there is an easier way.
Usually, I first roughly place and rotate the camera as desired ( I find it easier to place the camera at a certain “height” before I do the following to “fine-tune” the orientation and rotation); then select (right click) the camera and press Numpad_0 to enter Camera view mode.
Then use the [g] and [r] keys (not at the same time 
) to line up and rotate the camera view.
Note: For rotating the camera view, after activating rotate mode [r], do a Middle Mouse Button click to free up another axis of rotation.
You can also track the camera to an empty.
Create an empty (Spacebar -> Add -> Empty)
Select the camera, hold shift and select the Empty.
Track the empty (Ctrl-T)
If the rotation of the camera is not correct, select it and clear the rotation (Alt-R)
OR
You can also use Fly mode.
Select the camera and press Shift-F to enter fly mode.
Alt moves the camera up (on the Z axis) and Shift moves it down.
Mouve the mouse to change where the camera is pointing.
Left click to move forward.
Esc to exit fly mode (return to the initial position)
Spacebar to exit fly mode (keep the position)
Martin