Helping a friend $500 computer.

[Taotaisei]

This is what I've thought of so far. I however don't have much experience with budget rig gaming.

She does not need an OS, Mouse, keyboard, or HDD. She needs all the other items though. She has a budget of exactly $500 and will spend no more.
She wants 1080p.
Plays very few games. At the moment only Skyrim, Portal 2, and A Ticket to Ride. She's states she'd be willing to expand if her current computer didn't suck.
Buying from US retailers.
If it's in the part picker list, she needs it.

http://pcpartpicker.com/p/29e1A

Thank you for your time and input.

[Deleted]

Well this was quite a puzzle to get you the best performance for your money

Either way this is what I came up with:

PCPartPicker part list / Price breakdown by merchant / Benchmarks

CPU: Intel Core i3-4330 3.5GHz Dual-Core Processor ($119.99 @ NCIX US)
Motherboard: Asus H81M-K Micro ATX LGA1150 Motherboard ($46.98 @ Newegg)
Memory: G.Skill 4GB (2 x 2GB) DDR3-1333 Memory ($37.91 @ NCIX US)
Video Card: MSI Radeon HD 7850 2GB Video Card ($109.99 @ Newegg)
Case: Rosewill FBM-02 MicroATX Mini Tower Case ($21.99 @ Newegg)
Power Supply: Rosewill Hive 550W 80+ Bronze Certified Semi-Modular ATX Power Supply ($34.99 @ Newegg)
Optical Drive: Asus DRW-24F1ST DVD/CD Writer ($15.99 @ Newegg)
Monitor: Asus VE247H 23.6" Monitor ($109.99 @ Newegg)
Total: $497.83
(Prices include shipping, taxes, and discounts when available.)
(Generated by PCPartPicker 2013-11-26 19:26 EST-0500)

You're relying on a few rebates but so was your current suggestion so I figured it was ok?

[n0cturnal]

Personally I would skip the DVD and get a better case or spend it on another part.

[Taotaisei]

Yes rebates are perfectly fine.

To extrapolate from your suggestion, the i3-4330, though it is 2c4t will perform better than the fx-6300 in most games? (Yes I know most games are 2 core and just starting to push past that.) If so, cool. I have no personal alliance to blue, green, or red.

[chazus]

The i3-4330 is a surprisingly powerful CPU considering it's price. I've been recommending it a -lot- lately as basically the only viable step down from the 4670K (I disregard the i3-4340 lately because for $40 more, it's only 100mhz... not worth it)