if you are buying a single laptop this is what i have to say
I have an HP DV6 6195 with a core I7 2630qm and an AMD 6770m. I use mine for both gaming and school work. It has a feature on it that switches between the Intel integrated graphics and the AMD6770m. this way it saves battery. It also a rather pedestrian looking laptop but it will run games like an Alienware. running on integrated doing school work i get 3 hours on the battery. if you are looking for the best of both worlds this is what I personally use.
This is just an idea but if you are planning to play some newer games such as Skyrim or BF3. you definitely want something with discrete graphics. It all depends on what your budget is.
if you are looking for 2 different laptops
for school: something with a low power processor (like a core I3 or even a Pentium ar an AMD fusion prosessor) and lots of battery life
for gaming: something with a powerful processor (core I5 and I7) and discrete graphics, as well as A large amount of RAM (at least 4GB) battery life shouldn't matter much as you will have the thing plugged in
Brett, you got the first one right, not the second one. You could easily spend a $1000 and get an Intel ultrabook with i7, 8GB RAM, SSD, and a whole bunch of others but it has Intel HD 4000. Whats your budget? I would recommend a y500.