Steve, you could certainly use SketchUp to do what you want and whether you want to make elevations or perspective views, making 3D models in SketchUp will definitely help you get the shadows sorted out. In fact you could use an exported image to trace over if you want. Furniture pieces could be very simple massing models for reference and you can draw in the details as needed.
SketchUp only has one light; the sun. But you can simulate multiple overhead light sources as in the following image by exporting more than one image with the sun in different positions. I softened the shadows using a blur filter in the image editor.
Or you could do simple and quick renders with lights (a table lamp, floor lamp?) in the view.
There are a lot of options available.
As for tutorials, I'd start with the videos on the SketchUp.com site. I did a video tutorial thing awhile back that is available through FineWoodorking.com but it is more directed toward drawing a single piece of furniture. The lessons would still be useful and when it comes down to it, drawing a room and placing stuff in it really isn't any different than drawing a cabinet and adding parts to it.