Let's Talk Tesserae
First off, "Tesserae" is a term for any object used in creating a mosaic; for instance, vitreous tiles, stained glass, found objects, ceramic tiles, smalti, etc.
For beginning artists with stained glass experience, I recommend starting with your stained glass scraps. Easy to cut with wheeled nippers and your other tools, it is fine in both interior and exterior mosaics. Don’t be afraid to add other materials to your mosaic along with your stained glass. I love the juxtaposition between saturated colors of stained glass and muted colors of stone - as well as smooth surfaces of stained glass and textured surfaces of sea shells.
Found objects are just what they say they are, objects you can find all around you. Pebbles, shells, sea glass, stones, almost anything you think is interesting can be used in a mosaic. Generally, you will use a thicker layer of thinset to imbed them into and these objects are usually not grouted, due to having surfaces that are not easily cleaned from grout.
Ceramic tiles are commonly used and easy to buy at home improvement stores or perhaps scraps from your local tile store. You can cut them with nippers, tile cutters or break them with a hammer. They come in a variety of colors and have a hard glaze on one side.
Smalti, millefiori, mirror, and other miscellaneous tiles are fun to use. They add great splashes of color and detail. Make sure you use an adhesive designed to be used with each of these - especially the mirror!
China is another material that is used frequently. Old dishes, cups, bowls, can be broken or cut and will give your mosaics a cool 3-D effect. Most dishes have curves to them, so you will have to take this into consideration before cutting and gluing it if you need a flat piece.
Hope you'll try out different materials and have lots of fun with your mosaics!