After a google search, I gathered the followig points.
1. Do not open ports on your router.
Do not use default admin password ( On day one itself I had changed the admin password

. ) Do not enable WAN Management. Keep your modem/router firmware up-to-date.
2. Use a modem/router with a built-in firewall. (A firewall will be needed only in case of direct cable Internet connection plugged into your system.)
3. There are thousands of hosts that do nothing but scan all possible IP addresses looking for weaknesses. It is a fact of life.
That is what a router/firewall is for. ((Only your ISP can filter out those for the range of IPs it dishes out, if it cares.)
4. Those may or may not be genuine attacks.
5. Did you check to see who owns the domains that are "attacking" you? It is a futile exercise. A hacker will keep shifting his IPs and trying from different domains from different locations.
As long as the logs are showing the attacks the router ( its firewall) is doing its job. ( This what I felt and told in my post#8 in response to Megahertz07's recommendation of ZoneAlarm .
"Even now I would believe my modem/ router effectively stonewalls any intrusions reported.( I have immense faith in NetGear )"
With these comments, I shall mark this thread as solved.