Just to bring this thread up to date, the new PC has arrived safe and sound and is connected to the internet by means of a Netgear DSL Router DG834G. Cracking bit of kit, isn't it? A wired ethernet USB adaptor to the old (my) computer and a wireless USB adaptor to the new (my son's) PC completed the job with remarkably little fuss as you had all said.
Having installed the hardware, XP's networking wizard made file sharing a doddle and although I haven't tried it yet, I believe the new PC has been set up to use the printer of the old PC.
Result
Thanks again for the advice.