Core I3 3220 @ 6.8k
Asus P8H61 M LX @ 2.8k
Corsair 4 GB DDR3 @ 1.2k
Total 10.8....
Getting those old components is not a way to go ...... Extend your Budget and you will see Good performance....
for the mentioned GPU, i3 wont be a mandatory stuff, given casual gaming is the primary need. Intel Pentium Dual Core G645 is almost same as a i3

would do fine at half the price.
Intel Pentium Dual Core G645 @ 3.3k
H61 based board @ 2.8k
DDR-III 1333 MHz 4GB @ 1.2k