Have a look in the Laptops section here on LinuxQuestions.
I have 2 Linux laptops myself and I built one for my mother.
1/ 2 year old Acer TravelMate 23xx with Intel 855 graphics & IPN2220 wifi. The main OS is Suse 10.2 and it has worked for 6 months with no problems. Before that I used Kubuntu 6 with no real problems but changed to Suse because it has more tools for configuration. Kubuntu is very good for a beginner, but on a laptop it can be harder to get the wifi & LCD display correct.
2/ My mum's 6 month old Dell Inspiron 1300 with Intel 915 graphics & Broadcom bcm4138 wifi. This is Suse 10.1 and she has had no problems, though she only uses it for e-mail and a bit of internet surfing. Only the wifi & display resolution were a problem and that was not difficult to fix.
3/ Very old (8 years!) Compaq Presario 2406 with Intel graphics. This has Kubuntu 6.04 at present, but I think I might try DamnSmallLinux instead. No wifi, and a Lucent softmodem which was difficult to get working. I network it with a Kingston KNE PC28T card which worked straight off.
The only difficult part of any of the installation's I have done is getting the wireless to work, and sometimes the display resolution, but the fixes are not really hard. Most things work straight off. USB keyboards and mice just work when you plug them in, though with a bit of tweaking you can make them better. Most displays work straight off, though I have had problems with widescreen (1280x800) laptops.
Apart from Kubuntu/Ubuntu, I have tried Fedora Core 6 which is good, but not as nice on a laptop, and recently I have been looking at PCLinuxOS 2007. This looks like it might be better for laptops than Suse, as it detected the screen and wireless on my Acer, installed any additional drivers and did the configuration all from the installer. It should be much easier to get started.
One bit of advice I will give you is to download GParted
and make yourself a Live CD. Use this for partitioning and as a rescue disk. It handles NTFS well, and I've used it to partition and resize with Windows 2000 Pro & XP.