I already have a good wireless router but I'm going to be getting Vonage.
Is it cool to just connect a regular wired router with a VOIP connector to one of my wireless router's wired ports? Will there be any issues involved security-wise?
The scenario you mentioned is probably the best way to do it. Vonage's "routers" are notoriously poor at routing. I have mine in the following configuration:
All of my PCs and such connect to the 871. I do not have any ports opened on the Cisco 871 for the Vonage, it just works. The Vonage "WAN" port is what I have connected to the 871.