Wired + Wireless Networking Help

I’ve googled until my fingers are sore.

Original Setup
I have a Netopia DSL modem with built in wireless router which I have bridged and connected to a Cisco/Linksys V016 16 port wired router. Internet works fine.

What I would like to do is simply add a wireless router and provide public internet access in the office.

Trial #1
I swapped to a non-router DSL modem, hooked that to a switch. I then connected the wired router to the switch and a wireless router to the switch. This didn’t work and all internet died.

Trial #2
I went back to the original setup and simply plugged a regular wireless router into (I tried the Internet 2 and regular port) on the 16 port router. My wireless device will connect, but, I can’t get on the web (and of course I don’t want anyone to be able to access the private wired network).

Can someone give me a direction. Here is an equipment list.

Netopia DSL Modem with Wireless built in Router
Non-Wireless DSL modem (no routing)
Linksys 5 port switch
D-Link Wireless Router
Cisco/Linksys 16 port wired router.

I would really appreciate any help with this – I wouldn’t be asking if I hadn’t already looked for a few days for a solution.