Since I've got yet another old pc kicking around, I was thinking about using one of the many linux firewall installs and connecting it to my router, to which the other three pc's I have connect to.
My question is if it's worth it - Would a dedicated linux firewall provide any extra security? Would it slow down my overall net connection? I'm currently using a linksys router and haven't had any trouble.
I just figure it'd be a way to put the old pc to use and maybe add a layer of security.
You wouldn't want to use both firewalls, you'd use one or the other.. so if you used an old PC to build a firewall, it should replace your Linksys box, not be used with it. The main advantage of doing this is that you have many more options where the Linksys box may otherwise limit you. For instance, I think Linksys only gives you about 10 port-forward entries and you're stuck. A custom firewall as you describe would allow literally hundreds.
A hardware router/firewall like what you've got, if set up correctly should provide 'reasonable' protection.
The distinction between a hardware and software firewall is just perception. A "hardware" firewall like the Linksys box is nothing more than a computer running software that performs the function of a firewall. The main distinction that people use to differentiate is that a software firewall is loaded on to a PC that has other functions (i.e. loading NIS on to a desktop system) and a hardware firewall is a computer (PC or otherwise) whose main or only function is to be a firewall. In this case, a PC loaded with Linux setup as a firewall would be considered a hardware firewall (and almost indistinguishable from the Linksys firewall, which depending on the revision is probably also running Linux).