I'm working with like a 400 maybe 500 dollar budget here. If I can get just the laptop for that price then a new graphic card or somesuch later, that would work too I suppose. But 400-500 for the laptop itself. Is there any way to make that work?
Of course a $500 dekstop will get you a better gaming experience, but if a laptop is what you require you will need to use an AMD APU. Usually signified by A6, A8, A10. A10 is the best offering out right now.
Intel graphics HD 300 and HD 4000 also run the game, however AMD has lowest priced budget builds. Of course, a refurb or used laptop will get you the best value and best gaming experience.