Before you purchase any machine, go and see what kind of support the manufacturer (or more importantly where you purchase it from!-Echos Ambucias advice!)
You can also search the net for troubles that others may be having with a prospective computer you may be looking at. Some laptops will jump out at you for the troubles others are having (search this site and you will see a common denominator Manufacturer with most troubles!)
As for specs, any machine that will run 10 will be fast enough, the most important part is how much RAM you get. I encourage you to get either 6 or 8 MB of Ram. 4 is enough to surf web, but not 2gb. DO NOT GET CHEAP WITH RAM SPECIFICATIONS. If you are concerned with cheap, go with high ram and small HDD (hard disk drive). 500 GB is nice, but 80 will do most surfing just fine!