ok, if its just for Minecraft i would recommend getting something like a:
-AMD A8-5600K
-8GB corsair XMS3 1333Mhz
-Just some cheap case
-a Western Digital 500GB Blue
-You wouldn't need a graphics ...

I'd recommend looking at PCspecialist for a good cheap custom PC if you don't want to build it yourself.

Define cheepish, also what exactly do you want to use it for?

Not much, its a bit old and the parts are not too good. I'd recommend either spending a bit more on an upgraded version or something different. You want at elast an i3 at 3.0Ghz or faster. The rams ok ...

If you want an AMD card then i would recommend a HD7770, there about 100-120 and should do what you want. I just wouldn't recommend getting a VTX3D one tho. Buy sapphire if you can.
But you also need ...

What kind of budget do you have, also any preference to AMD or Nvidia?

Processor: AMD PhenomII X4 965 O.C. 4.017Ghz
Graphics card: Sapphire AMD HD6950
RAM: 8GB Corsair XMS3 O.C. 1600
PSU: Corsair GS600 600 watt
SSD; Kingston v100 64GB
HDD: Western Digital 2TB Caviar ...