Suggest you look at what cheap at bestbuy and see what CPU and video they have then goto www.notebookcheck.com and see gaming framerates. Make sure you liek the keyboard feel. Plan on getting external gaming mouse.
Here are a bunch of A8 units. (Check for framerate on A8 and see if it's good enough for you) http://www.bestbuy.com/site/olstemplatemapper.jsp?id=pc...||414d44~~nf546||414d442041382d536572696573&list=y&nrp=15&sc=abComputerSP&ks=960&usc=abcat0500000&sp=-bestsellingsort+skuid&list=y&iht=n&st=processingtime%3A%3E1900-01-01&gf=y
IF you post screen size, preferred brand, etc. people might get more specific.
To this question, most any laptop with a dedicated graphics card would do just fine. I mean you only intend to spend 700usd tops, so you cant get higher end.
Here I cant link you to any particular one (im from Chile, dont know where to find your retailers) but as a general advise:
For about 1000USD (maybe less) you can get an 15.4" HP M6, which is a 2nd gen APU A10 (Trinity, 4cores) with a dedicated HD7550D, in dual graphics mode with the IGP. Pretty solid performance in most mainstream games, and long battery life. Review here in TomsHardware.
For about 800 you should find an ASUS N-series, a 15.4" Core i5 with a dedicated GTX540 or 550 (I cant remember). I really trust ASUS, its very probable that this notebook wont get too hot, and its CPU power is considerable. If you get any other brand like samsung or HP, odds are that you will find manufacturing defects (overheating, bad solderings etc). Besides, asus has an amazing warranty
If you want something even lower end, you should go AMD (with their, honestly amazing APUs) but really, if you buy an under 600USD machine, you will probably NOT enjoy the experience, and will need to upgrade sooner