You can certainly use squid. You can also use Apache. There is a container <Proxy> you can use together with directives ProxyRequests and ProxyVia (you almost always need this) in httpd.conf.
In fact, I have it set up to do that on my home server. I use the following to get it to work for any machine in my home LAN, but on port 8080 (I have 'Listen 8080' elsewhere in httpd.conf):
<IfModule mod_proxy.c>
ProxyRequests On
ProxyVia On
<Proxy *:8080>
Require valid-user
AuthName "ClosedProxy"
AuthType Basic
AuthUserFile /home/mejohnsn/serverPwdFileBasic
Order allow,deny
Allow from 192.168.0.0/255.255.255.0
Satisfy Any
</Proxy>
</IfModule>
And I used htpasswd to create the one user and password in serverPwdFileBasic
Now for what you are doing, you don't need all that complexity: I was trying to get it to work without password (authentication challenge) for machines inside, but with challenge for machines outside. But for machines outside, I get the challenge, yet authentication fails even when I do enter the right user/password. So it is still safe from hackers

But this will be the topic of another post.
Don't forget to open up port 8080 on the firewalls on all machines inside your LAN. Or change it to port 80, if as likely it is already open.
The article at
http://www.devshed.com/c/a/Administr...roxy-Server/2/ on using Apache as a proxy server is pretty elementary, but still pretty good. I lifted a lot of the above config from there.