All good choices. I like the USB HD adaptor idea and of course the flash drives are great things to have around for anything - and they work virtually anywhere.
(under 1.00)
If the old computer has a CD burner - create a disk - and copy it onto the new machine.
(free if you have cable(s))
This one takes some minor OS/networking skills:
If both machines have a NIC (network interface card) all you need is either a crossover cable or with a router , 2 standard ethernet cables. Share the drive on the old PC and copy away via \\
your old computer name in My Network Places address bar (or internet explorer's)
(Free - must have no fear of wires & screwdrivers & delicate electronics) - Memetic's got it:
You could just plug the old hard drive into the new PC as a slave drive.