From what I understand, you want to visit some websites and not have them log your IP address. A personal firewall or NAT would not work since they would still see your external IP address and still know it was you by going to your ISP. If your not doing anything illegal, you can use a anonymizer. But if you are doing something illegal and you get caught the anonymizer will tell on you.
What I do when I want to visit a website and not have them log my real IP, is I run AOL on top of my normal connection, that way you are going through AOL's proxy, and any IP that is logged will show up as a AOL proxy. It only costs $9 a month for AOL bring your own access.