I am a bit puzzled at the specs listed....
I am thinking that 512K and 120MB would do it.
512 K of what? There's not much measured in modern computers at 512 K, other than the L2 cache, which is not a huge consideration.
And if you are referring to the RAM with the 120MB figure, I think you mean 128, and that is WOEFULLY inadequate for the latest operating systems, including XP. I cannot imagine buying even a basic PC with less than 512MB of ram, regardless of the brand or operating system used. This is particularly important if you will be using any video components.
If you absolutely MUST have a Windows based PC, here are the specs I would suggest you look at (and stay away from E-machines. There is a reason they are cheaper...):
Pentium® 4 Processor at 2.20GHz
256MB DDR SDRAM at 333MHz BARE MINIMUM, if the machine has a separate video card, (512MB if "shared memory" is used for video, which I strongly discourage).
40GB ATA/100 Hard Drive - bigger if you can afford it - the more empty space on the drive, the happier the OS is....
DVD/CD-RW combo drive - you will want the CD burner portion for back-ups and other recording needs. The DVD side would be helpful for watching movies and some software titles..
32MB NVidia or Radeon video card as MINIMUM, 64MB would be preferable.
Windows XP Professional - especially if you plan on a home network.
You really don't want to scrimp on RAM - it is one of the most cost effective "upgrades" to a computer and it's performance. Even if you think you will never use a lot of ram, the computer will run appreciably faster and more stable if you have extra.
As I stated to begin with, I highly reccomend a Macintosh for your purposes - it will be easier to network, and simpler to operate. For education and kids, it's hard to beat an eMac or iMac (flat panel). Both can be had reasonable inexpensively.
Also, the Macintosh platform enjoys the longest "useful life" of any platform. I have a 9 year old PowerMacintosh 7200 in my band room that still kicking and working.
If you truly have to have a Windows based PC, then I strongly urge you to get as much machine as you can (the minimums I listed should get you headed in a reasonable direction).
Good luck.