John -
Let me help you here. First, do not confuse the Tone Ring with the Wooden Rim. Here is the difference:
Tone Ring - is located inside the rim. It supports the head (usually mylar plastic drum portion) of the instrument. The tone ring is either a flathead or archtop. The Flathead provides a deeper tone and an archtop provides a brighter tone.
Rim - Can be made out of wood or metal. Today's wooden rims provide excellent sound if you get the right rim. Rims come in various types: Tony Pass, Old Factory Floor, Cox Maple Wood rims (to name a few). Some of these rims are made of wood that is hundreds of years old and provide the rich tones similar to a pre-war instrument. Rims of this type however, will not be found in budget banjos under $1,000. These rims alone cost around $500.
The pot assembly of the banjo consists of the tone ring, rim, tension hoop, resonator and other parts.
Hope this helps. When you are ready to buy, let me know and I will get you a decent banjo for the money.
Dave