If you have firewall and antivirus as you describe then you should be safe from all but the most determined hacker. You can also run a regular check using something like malwarebytes (free version) to scan your system to ensure that nothing has got through the net.
1. You don't have to install Norton if you are happy with what you have.
Your ISP cannot force you to change your AV Program.
2. It is not recommended to have 2 AVs ( Norton and Avast ) installed in the same machine. They will create Conflicts and you will end up getting less protection then having just one AV program.
3. I would not recommend Norton at all. Did your ISP make you pay for it?
I have a Win 7 Home Premium 64-bit.
All I am using are.....
Avast for real time protection and Malwarebytes (free edition ) for on-demand protection.
That's all I need.