I am in the UK so no idea of prices in USD but...
I am doing a rig for my nephew and it is:
Intel Core i3 4130
Asus H81I-PLUS Motherboard
Corsair CMX4GX3M2A1600C9 XMS3 4GB (2x2GB) DDR3 1600 Mhz
MSI AMD R7770 1GB DDR5 PCI-E (however this can be swapped with a R9 270X as your budget is higher)
Cooler Master Elite 120
500w PSU
I only consider Mini ITX as bit tower are just too big too heavy...