Reddit mentions of Acer Aspire V Nitro 15.6-Inches Laptop (Intel Core i7-4720HQ processor Quad-core 2.6GHz with Turbo 3.6GHz, 8 GB SDRAM DDR3, 1 TB HDD, Windows 10) Black

15 inch screen, cheap, great battery life, will run Skyrim no problem. Id recommend getting this and then just a cheap external hard drive to store all of your mass media, and a 20 dollar usb optical drive for when you need it. Its the best bang for your buck solution. Nothing else gaming grade I'm aware of comes close to this things battery life. Im not sure how important that is to you though.
https://www.amazon.com/gp/product/B01ES76HQQ/ref=ox_sc_sfl_title_1?ie=UTF8&psc=1&smid=A3GQ8W9AF8L0NJ

If its not as important, this Acer will give you an estimated 5 hours of battery (not while gaming though), plenty of internal space, an optical drive, and will run skyrim no problem.
https://www.amazon.com/gp/product/B01FIL864W/ref=ox_sc_sfl_title_4?ie=UTF8&psc=1&smid=A16YSFOH31M2GC

My year old Asus runs it at about 60fps (with dips in areas of high traffic and certain dungeons) 1080p with most of the settings on 2-3 and no anti aliasing. It's got an intel core i7-4720HQ, 8gb of ram, and an Nvidia Geforce GTX 950M. A 940M could probably run it a bit slower/lower settings, but I can't guarantee it (laptops with 940Ms seem to be around $650 on Amazon).

This looks like a slightly better version of mine for just under $800:
https://www.amazon.com/Acer-Aspire-Nitro-15-6-Inches-i7-4720HQ/dp/B01ES76HQQ/

Or this if you prefer an SSD:
https://www.amazon.com/dp/B015PYYDMQ

In between the two there's this which nearly the same model as mine:
https://www.amazon.com/Asus-R516UX-Performance-i7-6500U-1920x1080/dp/B01HXEZN8O/
I love my Asus laptop but their support stinks. Looking at Asus laptops just sub-Rog and looking around for a deal on them is a decent way to find a good model for a good price.

Probably the best laptop for the price, check this out..
https://www.amazon.com/Acer-Aspire-Nitro-15-6-Inches-i7-4720HQ/dp/B01ES76HQQ/ref=sr_1_3?ie=UTF8&qid=1473529818&sr=8-3&keywords=Acer+aspire+v+nitro

I recommend the Acer Aspire V Nitro

This is probably as good as you're going to get for a low-cost laptop. You might be able to get a steady 30 FPS at minimum settings. Going a little more expensive will net you more performance and an SSD for good Windows performance. The sweet spot in price/performance ratio would probably be this, but the lack of an SSD pains me. If I were to buy a gaming laptop, the lowest-end model I would get would be this Asus ROG.

The PSA says to but the Acer Nitro, so would this be better for the price?