Cleaning your jewelry at home is a great idea!
First of all, do no harm! The gentlest approach is always the one to try first. A soft brush and some mild soap can do wonders. When I say mild soap, I mean anything you might put on your skin. No harsh cleaners needed here. Everyday cleaners that will harm your jewelry are bleach (it discolors silver and attacks the solder that holds gold jewelry together) and cleanser (think Comet, Ajax and even Bon Ami) because they will take the finish off many stones and ruin the polish on fine metals. Alcohol can ruin pearls. If you have really soiled jewelry and just must use a strong cleaner, a few drops of amonia in soapy water can help cut through the hand lotion and dirt hiding the light of your gems.