Need help picking parts for light gaming and heavy drawing. Professional opinions appreciated!

Not really. This is vastly better adn worth every extra penny:

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($110.99 @ SuperBiiz)
Motherboard: ECS H110I-C4P Mini ITX LGA1151 Motherboard ($55.98 @ Newegg)
Memory: *Team Elite Plus 8GB (1 x 8GB) DDR4-2133 Memory ($34.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.49 @ OutletPC)
Video Card: PowerColor Radeon RX 460 2GB Red Dragon Video Card ($99.98 @ Newegg)
Case: Cooler Master Elite 130 Mini ITX Tower Case ($34.99 @ Newegg)
Power Supply: Antec 450W ATX Power Supply ($36.99 @ SuperBiiz)
Total: $423.41
Prices include shipping, taxes, and discounts when available
*Lowest price parts chosen from parametric criteria
Generated by PCPartPicker 2016-10-11 19:46 EDT-0400
 
ASRock AM1B-ITX has a PCI express x16 slot but it only runs at X4. You will not be able to run a regular video card from that slot and expect it to function correctly.

AMD Athlon X4 860k
http://www.newegg.com/Product/Product.aspx?Item=N82E16819113410&Tpk=N82E16819113410

G.SKILL Sniper Series 8GB (2 x 4GB) 240-Pin DDR3 SDRAM DDR3 2133
http://www.newegg.com/Product/Product.aspx?Item=N82E16820231519&cm_re=DDR3-2133-_-20-231-519-_-Product

GIGABYTE GA-F2A88XN-WIFI
http://www.newegg.com/Product/Product.aspx?Item=N82E16813128663
 
Here's another i3-6100 build with nice case.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Core i3-6100 3.7GHz Dual-Core Processor ($110.99 @ SuperBiiz)
Motherboard: Asus H110M-A/M.2 Micro ATX LGA1151 Motherboard ($49.98 @ Newegg)
Memory: Kingston HyperX Fury Black 8GB (1 x 8GB) DDR4-2133 Memory ($37.50 @ Amazon)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.49 @ OutletPC)
Video Card: Gigabyte Radeon RX 460 2GB WINDFORCE OC Video Card ($108.25 @ B&H)
Case: Apevia X-PIONEER-PK ATX Mid Tower Case ($47.99 @ Newegg)
Power Supply: SeaSonic S12II 430W 80+ Bronze Certified ATX Power Supply ($39.99 @ Newegg)
Total: $444.19
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-10-11 20:14 EDT-0400

Edit:
And a solid DDR3 build closer to the budget.

PCPartPicker part list / Price breakdown by merchant

CPU: Intel Pentium G3258 3.2GHz Dual-Core Processor ($76.98 @ Newegg)
Motherboard: Gigabyte GA-B85M-DS3H-A Micro ATX LGA1150 Motherboard ($40.98 @ Newegg)
Memory: Team Vulcan 8GB (2 x 4GB) DDR3-1600 Memory ($33.99 @ Newegg)
Storage: Western Digital Caviar Blue 1TB 3.5" 7200RPM Internal Hard Drive ($49.49 @ OutletPC)
Video Card: Asus GeForce GTX 750 Ti 2GB Video Card ($92.98 @ Newegg)
Case: Apevia X-PIONEER-PK ATX Mid Tower Case ($47.99 @ Newegg)
Power Supply: SeaSonic S12II 430W 80+ Bronze Certified ATX Power Supply ($39.99 @ Newegg)
Total: $367.40
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2016-10-11 20:23 EDT-0400

And also the comparison between the two.

Userbenchmark PC Build Comparison

Baseline Bench: Game 38%, Desk 54%, Work 30%
CPU: Intel Core i3-6100
GPU: AMD RX 460
HDD: WD Blue 1TB (2012)
RAM: HyperX Fury DDR4 2133 C14 1x8GB

Alternative Bench: Game 28%, Desk 50%, Work 25%
CPU: Intel Pentium G3258
GPU: Nvidia GTX 750 Ti
HDD: WD Blue 1TB (2012)
RAM: Corsair Vengeance DDR3 1600 C9 2x4GB
 
Solution



I am conflicted between Rx 460 and 750 Ti.

What I do know is that 750 Ti is about to be outdated soon or later since it's 2+ years old. I am surprised that 750 Ti is holding its ground even against Rx 460.
 



Could your RX 460 and rest fit into Cooler Master Elite 130 case?
I don't think pink case is good for my sister.
 
Short answer: No.

Long answer:
Cooler Master Elite 130 is a mini ITX case and supports only mini ITX MoBo.
MoBos in both of my builds are micro ATX (larger than mini ITX).

For switching out the cute case i picked, smallest case you're looking is a micro ATX slim or HTPC case.

List of HTPC (by price),
pcpp: http://pcpartpicker.com/products/case/#t=11&sort=a8&page=1

List of micro ATX slim (by price),
pcpp: http://pcpartpicker.com/products/case/#t=8&sort=a8

List of micro ATX mini tower (by price),
pcpp: http://pcpartpicker.com/products/case/#t=6&sort=a8

List of micro ATX desktop (by price),
pcpp: http://pcpartpicker.com/products/case/#t=5&sort=a8

Or you can always go with the same case but in different color.
Black/blue, pcpp: http://pcpartpicker.com/product/NNPzK8/apevia-case-xpioneerbl
White/blue, pcpp: http://pcpartpicker.com/product/GfPzK8/apevia-case-xpioneerwht