Depending on what you're looking for, realistically it's difficult to get a laptop for light gaming, unless you're going to be playing 2D Indy games on the steam marketplace.
Here is an Acer Aspire that I would recommend for the 840M, if you need to meet budget.
http/www.amazon.com/Acer-Aspire-V3-572G-54S6-Gaming-Laptop/dp/B00MM2WA8O%3FSubscriptionId%3DAKIAI62SSPLIHX7AR6PA%26tag%3Dsnapsort-623-20%26linkCode%3Dxm2%26camp%3D2025%26creative%3D165953%26creativeASIN%3DB00MM2WA8O
http
/www.newegg.com/Product/ProductList.aspx?Submit=ENE&N= 100025325&IsNodeId=1&bop=And&Order=PRICE&PageSize=30
There's a list of comparable gaming systems, and it looks like most of them start at 700+, with 750 average for an 840M, which I would consider fit for light gaming. 820M is practically as basic as it gets, being only slightly faster than integrated. The 850M has roughly 300% more real world performance over the 840M, for example, bioshock infinite has 13FPS on the 840M and 29FPS on the 850M. I would recommend an 850M with a AMD chipset for light gaming and school work, but I don't expect you to spring for it:
http/www.newegg.com/Product/Product.aspx?Item=N82E16834232132&cm_re=850m_laptop-_-34-232-132-_-Product
http
/gpuboss.com/gpus/GeForce-GTX-850M-vs-GeForce-840M