You probably wouldn't need a case large enough to carry a D-SLR size camera however this camera is slightly larger than a standard compact. The best thing would be to take the camera to your nearest BestBuy and test fit in a few cases.

You'll need to get one that fits the inner lens size. That number is usually marked on the lens on the inner area next to the glass as a ## with a circle and a / through it. Common sizes are: 46, 49, 52, 55, 58, 62, 67, 72 and 77mm.
If it is the 18-135mm lens it might be filter size 67mm.
If it is the 18-55mm lens it could be the 52mm filter.
Lens caps follow the same size as the filters.

Most all HD camcorders also have a SD setting.
The image quality should look a bit better due to it being digitally captured and it is a direct playback. Also the HD sensor is going to have more lines of resolution information giving you a better, sharper image.

There is a very large selection of lenses that work with the Canon 40D. Canon lenses and many lenses made by other manufacturers such as Sigma and Tamron.
If it is a EF...not EF-S...mount lens it should work fine.
There might also be some lenses designed for full frame cameras that won't work on the 40D also.