Hello,
The other computers on the family network would access the internet though the linux box. Simply give the other computers the default route (gateway) of the IP number of the linux box's LAN card, and you should be set.
Time for a little ASCII ART. Pardon the yuck here, but it will help.
WAN CARD OF LINUX BOX --> CABLE MODEM ---> INTERNET
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an.external.ip.address (23.11.142.7)
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Firewall running on Linux
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an.internal.ip.address (192.168.1.1)
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LAN CARD OF LINUX BOX --> HUB --> Computer1
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------> Computer2
Computer 1 could be 192.168.1.5 and computer 2 could be 192.168.1.10
You will need to tell the firewall on Linux some information about packets to allow, and which ones to drop. Check out information on IPTABLES or SONICWALL.
And if you want the linux box to be a peer, along with computer1 and computer2, then yes, you could access it
http://internalnumber or if you have it in DNS somewhere,
http://internalname
We are starting to get to the advanced stage of network design in the house.
Christian