For piggy back shots just open the lens as far as you can and still get nice round stars at the edges (may have to stop down one or two stops), set the zoom to fit the field you want to image and if you are well polar aligned (needs a wedge) you should get nice star fields in 5 to 10 minutes. Stacking several will reduce noise. Set the camera in RAW mode so no data is lost. Set the ISO as high as you can without noise getting into the image. Ditto the exposure time. At least with a digital camera you don't waste film and can keep trying until you get the results you want. Not having a DSLR I don't know what's optimum for your camera.

Without a wedge you might get by with lots of shorter exposures if taking near the meridian. The problem is the field rotates as an alt-azimuth mount tracks the sky so each image will need to be rotated slightly to keep the stars from turning into arcs. With an equatorial mount that isn't a problem.

For best results you'll want to have the camera's IR cut off filter replaced with one that doesn't block Hydrogen Alpha light as the factory one does. Replacing it does void the warranty however. Hutech offers this service.
http://www.sciencecenter.net/hutech/canon/index.htm

For planets you will remove the lens and replace it with a T adaptor. Use a barlow lens or two stacked to enlarge the image to about f/30 or so. At f/10 you'll want a 3x barlow minimum to get the image scale needed for planets. For the moon you'll want none for the whole moon then add one for higher powers. For this the alt azimuth mount is fine. Exposure time is short so you don't have to worry about field rotation as you do with deep sky shots.

Later as you gain experience you can add an off axis guider and take long prime focus deep sky shots. Though to get that shot of M31 you'll want a small, high quality refractor such as a ED80 type mounted on your LX200. Use the LX200 to guide with another CCD. You'll only be able to fit a small part of M31 into the field of your LX200 even with a telecompressor. Something you will want when you are ready for that type of photography.

Find a club in your area. Most have experienced astrophotographers and can give you a lot of hands on help that will greatly reduce the learning curve which can get very steep.

http://www.astronomyclubs.com/
http://www.skyandtelescope.com/community/organizations

There are a few books on the use of DSLRs but not using one I'm no up on these. Maybe someone will give you a lead there. Still the fellows in a local club are the best way to go if at all possible.

Rick