You shouldn't set a default gateway in your router since you are routing. The static default route is good enough.
I assume you have private addressing for your network. You will need to configure NAT to translate your private addresses to the public address of the WAN interface. Google, and other Internet sites, cannot send return traffic to private addresses since the private addresses cannot be routed on the Internet.
Also, you really, really, really, need a firewall. Every time I set up something connected to the Internet, within 5 minutes, I can log a dozen attempts to break into what I just set up.
Edit based on the comment that there is a router between the Cisco router and the Internet:
Your Internet router doesn't know about the network behind your Cisco router. Somehow, either using a static route or dynamic routing between the two routers, it need to know that traffic for the
192.168.10.0/24 network should go to
You could also NAT on the Cisco to accomplish this, but that in not an ideal solution.