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
Desktop machine: 2 x Opteron 246, Asus K8N-DL, 2GB PC3200 ECC Reg., XFX GeForce 6600GT, 74gb WD Raptor, 2 x 19\" LCDs, Windows XP x64
Server machine: Intel P4 3.0GHz 2MB EM64T, ECS i865pe, 1GB PC3200, 36gb WD Raptor, Windows Server 2003
Laptop: Dell Inspiron 9100 (Intel P4 3.2GHz 1MB Prescott, i865pe, 512MB PC3200, Mobility Radeon 9700, DVD+R/DL Burner), Windows XP
Linux: P3 450Mhz, 386MB ram, Slackware 10.1 (Running mySQL/Apache)