Welcome to the Tech Report!
$400 can be a tough price point, especially when you include the cost of Microsoft Windows. You might consider a refurbished or scratched-and-dented Dell Inspiron 660 from the outlet store
before you commit to building it yourself.
You can expand your list of vendors by including Directron and Amazon in addition to Newegg.
Shopping at Newegg, you can keep an eye out for combination deals. For example:$110
AMD A8-5600K socket FM2 quad-core 3.6 GHz APU with Sim City coupon$87½ -25 combo -10MIR
Gigabyte GA-F2A85XM-D3H socket FM2 micro-ATX motherboard
That ends up getting you a better motherboard (A85X chipset, +1 PCIe slot, 4 memory sockets, USB 3.0, SATA 6Gb/s) and a faster processor for not much more than the $155 motherboard+CPU that you have on your list.
To get good performance from your socket-FM2 Trinity processor, you should use PC3-14900 memory (DDR3-1866, CAS 9 or lower, 1.5 V or lower), like this:$68
2x4 GiB G.Skill F3-1866C9D-8GABor $65
2x4 GiB GeIL GEL38GB1866C9DC
Do you have keyboard, mouse, monitor and speakers?
I wouldn't suggest a no-name power supply if the budget weren't so tight, but you might be able to shave $45 off of your build with something like the $55 -15 code "EMCXRWX44"
Rosewill R363-M-BK which includes a power supply. Otherwise, consider the $55 -15 code "EMCXRWS92"
Rosewill LINE-M. This well-reviewed
case includes front panel USB3 and excellent ventilation for less than the $45 -10MIR case that you have on your list.