To get the whole thing in a desktop PC that will run it fine, you are looking at around 700 bucks. I'm sure you can find places to shave here and there or possibly going up to R9 270 or R9 270X which would be a major benefit at 1080p ( but you are looking at $30-50 more. But this one should work. It also pretty much does everything else you'd want from the PC.
Display and Win8.1 included. Keyboard and mouse are personal preferences so those she should choose herself anyway.
PCPartPicker part list:
http/pcpartpicker.com/p/PzKrLk
Price breakdown by merchant: http
/pcpartpicker.com/p/PzKrLk/by_merchant/
CPU: AMD Athlon X4 860K 3.7GHz Quad-Core Processor ($74.28 @ OutletPC)
Motherboard: Gigabyte GA-F2A88XM-D3H Micro ATX FM2+ Motherboard ($58.99 @ NCIX US)
Memory: G.Skill Ripjaws Series 8GB (2 x 4GB) DDR3-1600 Memory ($62.99 @ Newegg)
Storage: Seagate Barracuda 1TB 3.5" 7200RPM Internal Hard Drive ($48.88 @ OutletPC)
Video Card: Sapphire Radeon R7 260X 2GB Video Card ($89.99 @ Newegg)
Case: Rosewill Challenger-U3 ATX Mid Tower Case ($49.99 @ Newegg)
Power Supply: EVGA 500W 80+ Bronze Certified ATX Power Supply ($34.99 @ NCIX US)
Optical Drive: Asus DRW-24B1ST/BLK/B/AS DVD/CD Writer ($16.98 @ OutletPC)
Operating System: Microsoft Windows 8.1 - 64-bit (OEM) (64-bit) ($89.98 @ OutletPC)
Monitor: AOC i2367Fh 60Hz 23.0" Monitor ($152.99 @ Amazon)
Total: $680.06
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-01-26 17:57 EST-0500
Laptops with much worse performance you can probably get in the 400 range. The ones which have even reasonable graphics, you are looking at the same 700 mark.
Such as this MSI model.