Do you run any servers on your WinXP machine? On the assumption that you are not, then by far the safest way to do things is to buy any reasonable network switch that supports DHCP and let that be your interface to the network for all machines. Then you don't need to configure internet connection sharing on the WinXP machine.
Note that I believe when you configure internet connection sharing, that WinXP automatically provides DHCP services to the machines connected to the 2nd network. Almost all Linux installs today will either default to DHCP or are trivially configurable as DHCP clients. Thus, adding the Linux machine to the network will be trivial. Ensure that the NIC is configured as DHCP and then plug it in.
I use my Linux server as my direct connection to the internet, but that's because I run several servers on my Linux server (I'm paying for a network connection that allows me to run any services I want, and I have a static IP address) and also so that I can run a packet filtering firewall on my Linux server to protect the rest of my network from external attack. In your case, an external network switch that provides DHCP would provide this protection for you -- the switch would be exposed to attack and nothing else. Only if they could hack the switch would they be able to hack into your network. (Of course, I'm ignoring viruses and trojans and spywhere here, most of which are installed by insecure web actions, via Email, or by otherwise tricking people into installing them.)
If you don't want to do this and you want the most minimal change to your current network, then as I said, I believe that ICS sets up a DHCP server. Just install Linux on the new machine, configure its NIC for DHCP, and plug it into that 2nd network. It should just work. I helped my parents set up a network much like this, and have connected my Linux laptop to their network with no difficulty.
EDIT: Yes, an article at Microsoft.com, Internet Connection Sharing with Windows XP, confirms that ICS does automatically configure a DHCP server on the host machine.