Advice: Cost effective "gaming" laptop

[Just1ChanceFree]

Hi y'all, I'm looking to get the most for my money and trying to keep it under $800 but I'm considering options all the way down the $200 Stream 11 or looking at older models like the Thinkpad T420 I found on Woot.

My priority is really gaming ability for cost. My wife wants to have something she can play games with me on, but I suspect she probably isn't super serious and I want to throw as little money into it as possible and still give her a pleasant experience in lighter-resource games. It will probably end up being an extra laptop for excel and modeling, so lightweight and portable is the secondary priority. Spec targets by order of priority:

Windows 7 or more recent windows.
CPU and GPU performance for the money invested; I have been using passmark benchmarks for comparison (CPU Link) (GPU Link) and ideally I want something in the 2500-4000 CPU benchmark range, and after that focus is on maximizing the GPU performance for gaming speed, but best GPU performances I can find in this budget are like ~500. My desktop from 2007 gets ~1000 🙁
4 GB RAM min, 6+ is ideal.
11-14 inch; ideally with full-size keyboard.
No brand affinity whatsoever. Touchscreen/SSHD/resolution is all perks, but don't care.

Any input on what models to look at would be great! Thanks!

 

[Eximo]

T420 are a bit long in the tooth. End of life on support as of 2013 or so. T430 was the last model in that line. More of a business laptop anyway. T420s and T430s were a little better. But neither came with GPUs other then 1st gen mobile i series integrated.

Here is a new basic laptop with some GPU performance:

http/www.newegg.com/Product/Product.aspx?Item=N82E16834314713

 

[Just1ChanceFree]

Thank you Eximo! That's a great recommendation. Any others come to mind? I'd love to price/spec compare with others with dedicated gpu at less than 15".

 

[Eximo]

Couple of others from Lenovo if you want the cheapest ones, Y series, but that jumps up to about $800

i5 or i7 with GT840M or M250 or better.