IF you want a solid network then why not buy a router/access point with an inbuilt modem. It is possible to use a pc to pc network but it puts more strain especially if you have 2/3/4 computers trying to use the internet through the "host" pc. I dont know where you live so i cant really recommend something (i live in the uk and have a linksys wag354g router which does all of the above and works like a gem - but its only available in the uk alst time i checked)
As for the pc itself it depends what your budget is.
For processor, any AMD Athlon 64 will be fine, but go for a dual core processor (X2 processor series) if you can afford it. (i have a 3000+ and it runs those games fine)
You want at least 1gb of RAM - there is a big improvement in performance from 512mb to 1gb of ram.
Video cards wise, if your on a tighter budget go for a 7600gt which offers good performance at a reasonable price. If you have more to spend then go for a 7900gt(x). Both those cards are Nvidia and will be offered by most custom pc sites i guess.
The rest of the specifications are really up to you, such as hard disk size (160gb +), cd/dvd writer drives, sound card, speakers/monitor (if you need them).
And i must remind you that building a PC is very easy and the people on this forum will help you should you get into difficulties.
80gb + 250gb WD HDDs
X-FI Xtreme Music