There may be a little bit of a paradox here, in that whilst it is eminently possible to get cheap lappies, they are geared towards wordy, admin, or netty types of things as opposed to the Formula 1 performance that leading edge games demand. Bleeding edge games won't be a problem.
Laptops that will take todays' and let's not forget -tomorrows or next years games - are available, but they will cost a packet by comparison and even then will have limited (and expensive) upgrade options. These lightning fast lappies also chew up batteries like they are going out of fashion. My own Acer is a 3.0G Pentium 4 and that flattens a big battery in about 45 mins. They are called "Desktop replacements" in the trade. Such a device ain't much cop for school or college.
Two things I would consider, might go something like this. Either two laptops and one "Gaming" desktop (Much cheaper and easier to upgrade as well) or even three laptops and a dedicated "Gamer" like a Playstation or whatever.
Final tip? Never trust a salesman. Get printed matter, so that if your machine does not live up to expectation (Really thinking battery life here) you can point to it. Claiming that a slaes person had told you A,B, or C will get you a shrug and nothing else.
Conan