Why don't you just tell us how much you are transferring?
If its < 700MB, burn it to CD.
If its < 4GB, burn it to DVD (if you have one).
If its > 4GB, you can either
a) Network the PCs
-- Long initial setup if you are unfamiliar with networking
-- Pretty fast transfer if you are using 100Mbit/Gigabit hardware.
b) Install the hard drive in the new PC
-- Quickest setup, but you may not want to open up the PC
-- Fastest transfer rates