I too would strongly suggest you run a personal firewall & AV scanner.
Given that you are using it on a 'secure' home network, free products should be fine.

You have loads of free ones to choose from, most of which are pretty effective, and are pretty efficient as well. On the PC you described, I would say it doesn't matter in the slightest what you choose if you are just using it to surf the net or use email, as you have just enough spare capacity for the free products out there. You won't really notice the difference, and better safe than sorry, as extra layers of security are always a good idea.

In terms of footprint, the HD usage won't be an issue as you are talking of a few Mb at most.
CPU/memory usage can be an issue, but you have just enough to spare for normal net usage.

When it comes to using it for stand alone games (DOS based or anything else), terminate your firewall & AV software.
You will then get virtually all your resources (CPU, memory) back.
If you want to use the net again, just re-enable them.

EDIT: The point in running a personal firewall is to prevent this PC screwing the other PCs on your internal network.
From some setups that have been suggested (i.e. nothing!), it is quite possible this PC will get a virus/worm, which could then be passed to the two other PCs on your network.