It depends what you want to use it for.
If just web browsing, word processing, etc., then a comparatively low speed processor will do. Make sure that it has USB2 ports though. And about 512Mb RAM. CD RW/DVD ROM, Ethernet port, modem. A hard disk size of about 40Gb is the norm.
For gaming, Image Editing, Video Editing, you need a relatively high specification machine, with lots (1GB at least) of memory (RAM), USB2, Firewire, independent graphics and sound cards, CD/DVD RW, preferably Dual Layer. Ethernet port and Modem (for faxing or dial-up connections). You will also need a large hard disk capacity, in the region of 80-120Gb, with fast access times, 7200rpm.
In any event, make sure that you get an Operating System disk (unlikely), or a "restore" disk.
Also check what software is included, unless you already have it.
Notebooks (or "laptops") are more expensive than their desktop counterparts. Prices vary, but
www.morgancomputers.co.uk
and
www.aria.co.uk
carry reasonable prices.
No, I do not work for them, though I have purchased from them in the past.