Well I'd buy an external hard drive, copy your data files onto that from your laptop, safely disconnect it, connect it to your new computer and copy the files onto it.
Depending how much data you have it will probably be cheaper than memory sticks and more reliable for making regular backups from your new machine.
Tamborine - how do you back-up your files at the moment? PLEASE don't say that you don't. If you do, you can just copy the files from your back-up medium onto the new laptop. If you don't back-up then I hope you don't keep anything important on your computer.