Only advice I can give as I know a bit about desktops but little about laptops is, for gaming unless its older games you're wasting your time. I'm sorry but unless you spend a very large sum of money they just don't have the graphic capability, even then they aren't as good as a desktop with a dedicated graphics card. Regarding your mums computer any will do really, all laptops will do what you ask of that. Personally I rather like Toshibas, 2 friends have had them for a few years and never had a problem. Set a price and look at what you can get as I presume you aren't talking about spending £1500 on each of the laptops.