PCPartPicker part list / Price breakdown by merchant
CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($110.99 @ SuperBiiz) Motherboard: Gigabyte GA-H170M-D3H Micro ATX LGA1151 Motherboard ($78.95 @ Amazon) Memory: Kingston FURY 8GB (1 x 8GB) DDR4-2666 Memory ($34.19 @ Amazon) Storage: Samsung 850 EVO-Series 250GB 2.5" Solid State Drive ($90.58 @ Amazon) Case: Corsair 200R ATX Mid Tower Case ($54.99 @ Amazon) Power Supply: SeaSonic 350W 80+ Bronze Certified ATX Power Supply ($31.99 @ SuperBiiz) Optical Drive: Asus DRW-24F1ST DVD/CD Writer ($13.99 @ Newegg) Total: $415.68 Prices include shipping, taxes, and discounts when available Generated by PCPartPicker 2016-07-16 15:11 EDT-0400
She really doesn't need 16GB of RAM. An i3 is more than enough for what she does and you don't need a cooler. The stock cooler should be fine.