You came to the right place for opinions and here's mine.
PCPartPicker part list / Price breakdown by merchant / Benchmarks CPU: AMD A4-6300 3.7GHz Dual-Core Processor ($49.38 @ SuperBiiz) CPU Cooler: Zalman CNPS8900 Quiet CPU Cooler ($24.99 @ Newegg) Motherboard: MSI FM2-A75MA-E35 Micro ATX FM2 Motherboard ($57.78 @ Newegg) Memory: Crucial 4GB (2 x 2GB) DDR3-1333 Memory ($37.24 @ Adorama) Storage: Sandisk Ultra Plus 256GB 2.5" Solid State Disk ($119.00 @ Adorama) Case: Fractal Design Core 1000 USB 3.0 MicroATX Mid Tower Case ($39.99 @ Micro Center) Power Supply: Corsair Builder 500W 80+ Bronze Certified ATX Power Supply ($29.99 @ Newegg) Total: $358.37 (Prices include shipping, taxes, and discounts when available.) (Generated by PCPartPicker 2014-05-23 17:39 EDT-0400)
I selected the AMD because it is an APU and it has a little more graphical umph than CPU's.
I chose the Zalman cooler because of it's performance, value and low noise level.
The motherboard is just a lower tier model from a trusted manufacturer.
Ditto for the RAM.
Unless your mother is ripping CD's or DVD's 256GB of storage should be sufficient. If more storage is necessary you can get a quality 1TB internal for US$50-60 or an external for about the same.
The case is an affordable and well built case with understated lines that appeal to the older set (I'm 44 y/o).
The PSU has much more power than is necessary but it is about the least expensive unit I could find with a reputation that I trust.
Good luck.