If you will ONLY be running Squid on the machine, I would recommend at LEAST the following:
Pentium MMX @ 166MHz
4 MB RAM
10/100 Base-T Ethernet card
I mean, if the machine will not be a workstation, just an HTTP proxy, then you could probably get away with a 486, but those machines have outdated BIOSes to wrestle with if you're using a modern HDD.
I have a 486DX 33MHz with 16 MB RAM running Slackware-current and it acts on my LAN as the WAN router, a local caching name server, and a light-duty local web server. It could probably run squid at the same time and be just fine. (It used to be my SQL server, but I moved that duty to my wife's workstation (don't tell her) to reduce latency due to the small amount of RAM on the 486.)
The room where this machine will live can get a bit warm, so need a machine that runs on the cool side and will not overheat.
One nice thing about legacy machines is that, as long as you keep the chassis well ventilated, they do not tend toward heat issues. A good reason to go with a Pentium MMX 166 is that it is essentially an emasculated version of the 200MHz chip, and therefore even less likely to have any heat problems.