look at micro center for there cpu and mb combos. looking at a g600 to a g2120. they run about 40-100 for the new ib 2120.
the msi g45 micro atx running around 100. there are cheaper mb but if you go to cheap then when you have the funds to replace a cpu or run sli or crossfire you cant if you go to cheap. if your old pc has sata dvd and hard drive you could reuse them.
myself i would sit on your funds till you had some more. there a point with pc gaming that if you go to low in funds your not going to get a good gaming rig. min video card would be a 560ti or the newer 660.
i would by a second hand pc... with slightly better spec than above. it would likely have an amd quad and a 98gt gfx or maybe a 250 or 260 but all together it would perfom pretty similarly to the above...
if it helps, i already have a case, dvd drive, and a hard drive.
i was thinking of this model, because it has a quad cores and its pretty cheap.
motherboard: ASRock A55M-HVS FM1 AMD A55 - £34
cpu: AMD A8-3870K Unlocked Llano 3.0GHz Radeon 6550 - £68
psu: LEPA B550-SA 550W SLI/ Crossfire Ready 80 Plus Bronze Certified with single 12v Rail - £40
HDD:Seagate Barracuda ST250DM000 250GB 7200 RPM 16MB Cache SATA 6.0Gb£40
4 gb ram
total £198/ $313
Go with the APU, and if you need more GPU horsepower you can buy later an AMD 8000 series when they arrive, the integrated GPU will shutdown by itself and making the a8-3870K run at ~65 watt, thus making it really quiet and efficient for pure quad core, which will run anything you throw at it quite fine, just make sure the app is quad core friendly.