If you cannot do the steps that I listed above:
from the router ping your Netgear router: should be good
from the switch ping the ip address your cisco router on g0/0: should be good
from the router show routing table and verify you see all the networks you've created. and verify you can ping a host in each vlan you created.
for each of your hosts, do they have the default gateway of the vlan you've put them into? if so you should be able to ping those default gateways of each host.
On your router, when you create a default route. it should point to the internal ip address of your netgear soho router.
You cannot accomplish this. You have to set this up step by step if you do not understand. First get your router to connect to the outside world. Second, get each of the vlans to connect to your router and have routes that will ping the router's interface connecting to netgear router. If you cannot get the switch to talk to the router, you will not accomplish the rest.
