The sheet should be stiff, but not thick. If the metal can be incised with a scribe and maintain that through burnishing, it is suitably thick. The usual problem is that the copper is too thick rather than too thin. Copper leaf can be very faint if a single layer is used. Placing several layers improves the colour, but often provides wrinkles. So the requirement is to get a thickness of copper that will retain its structure, but not be so thick and stiff as to hold the glass up during the fusing process. The spaces under and over the copper give the opportunity for bubbles to form.
Do not use the copper foil as used for stained glass applications. The adhesive backing gives a black colour and many bubbles, or sometimes a single large one.
Copper sheet normally turns burgundy colour when oxidised.
To keep the copper colour, clean the metal well metal well with steel wool or a pot scrubber. If you use steel wool, wash and dry the metal before fusing.
Reduction of air contact with the metal helps to retain the copper colour.
Coating the copper with a borax solution will keep the copper colour better and help the copper to stick to the glass when being fused.
Apparently there are some compounds to add to the surface of the copper to turn it green. For example, vinegar is a good source of acetic acid used to give copper verdigris. Whether this is stable at kiln forming temperatures is questionable.