You might want to try installing squid on one of your dedicated machines and run it as proxy-only, that is if you don't want to store the pages you are viewing.
Then just configure your browser to point to that machine as its proxy. No need to configure your router to redirect traffic on http port to your proxy to simplify things.
Just make sure you configure the ACLs properly so it will not abused and used as a public proxy server.
Hope this helps.