|Is your cable modem a combination unit? (ie: combo modem/router/wireless access point) If it is, then you can do this with the equipment you have now. Otherwise, you would need to buy a second router in order to create a second, separate, network.|
If you can afford a second router, I would buy one and then you would setup your "public" wifi network on the router connected directly to the internet, and your private network would hang off of the second router you'd connect to that first router.
For more info on how it's done simply click on my name above in this response and read my “how-to” guide titled, “Add a second Router to your LAN”
You would want to use "version 2" from my guide wherein you interconnect the two switches LAN port to WAN port
It matters not how straight the gate,
How charged with punishments the scroll,
I am the master of my fate;
I am the captain of my soul.