Hi lib
I suppose you'd be looking at a minimum of 100Gb + hard drive these days (the storage capacity of your computer) not to be confused with RAM memory which is normally 256mb, 500mb 1Gb, 2Gb etc
If i had a lot of data - photographs and music etc, i'd invest in a external hard drive - i saw an advert for one - 1Tb (terabyte or 1000Gb's) for £87 +vat - amazingly cheap but anything above 350Gb would be worth having.
They connect via a usb socket so just connect to the old PC, transfer/copy everything across and then plug it into your new pc and copy across etc or keep it on the external hard drive as a back up - always useful.
SOme come with extras like a one-touch button that automatically updates any files changed since last recorded etc as a back up device.
Laptops may have smaller hard drives (memory) than tower systems but with external storage so cheap and such a good idea, then it isn't a problem and could just be a blessing in disguise if you ever 'loose your data'.
I have a 240Gb hard drive on my machine - can't see me ever filling it.
Hope that all helps - i'm sure far more qualified people than I will 'tch - tch' at my basic suggestions above.
I'd worry more about processor and ram - go for a 2Gb min if you can afford and as fast a processor as you can afford - avoid celeron as they do tend to be slower than their Intel and AMD athlon counterparts.