Answer for network equipment upgrade help

Yes, the FVL328 was released in 2003. So the technology is 12 years old! Just about anything new will run circles around this router.
The modem is DOCSIS 3.0, so it should handle today’s high speed services with no problem. Unless it is malfunctioning, I would think it should be fine left in place.
It is actually fairly difficult to find a mainstream router without wireless capabilities. Unless you have a very specific need for a VPN, I think just about any wireless router should handle your needs. I usually recommend a router like the Linksys EA3500 at a baseline. 
Let us know what you end up doing and how it works.