I use a network at home as well.
The things I have always kept an eye on:
1) hardware. tempuratures - cpu, gpu, chipset usually this is as easy as having a good (and quiet) case fan.
2) software. Anti-virus is a must www.free-av.com
I recommend it to everyone because they update it mutiple times per day - free for personal use.
Anti-spyware in the network situation especially, you need this. Scan weekly. AdAware is a popular one, and the microsoft one aparently works too.
3) firewall. firewall your computer from the rest of the network to prevent internal spreading of evil software, not just for exernal hack prevention. the winXP one works fine, and SELinux (security enhanced linux) is even better. A hareware firewall such as an old computer running a light-weight OS can also be set up to block advertising servers.