So, by focusing only on the transfer of actual data and not applications or app settings you can save yourself a lot of headaches.
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The most efficient method is by uploading your data to a network share (or make the old computer's drive available as a share) and then, once the new machine has been brought online and joined to a workgroup, domain or other sort of organizational unit, upload your data to its new home.
Many home users don't have this option and so it's often best to use a technique that accomplishes the same thing as network transfer but without the network.
For example, you might use a USB or firewire external drive. This would allow you to copy your data to a neutral location, off your existing machine, ready to be transferred to the new computer (remember, programs are replaceable since you can re-install, but data is often irreplaceable and should be treated as such).
Also, if you're very hardware savvy and have a spare hard drive of sufficient size already handy, you might install this in a "slave" configuration - transfer files to it then remove it from your old machine and install it in your old as a data drive.
Of course, this is much more work than simply using an external drive (USB and or firewire interfaced) as a data transfer device.
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If you want to preserve and transfer the "look and feel" of your old desktop you'll have to re-install your apps and then selectively copy the contents of your old computer's c:\documents and settings\<username> folder being careful to avoid files such as ntuser.dat (assuming this is a Win32 machine), the contents of the temp and ie5 folders and other unneeded objects.
This operation is a large topic all by itself that I can go into in some depth if you need.
But, if all you want to do is transfer data I would use a network if that's an option and an external drive if a network is unavailable.
.d.