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Well even though minecraft isnt the most demanding game on the market, doesnt mean you should run it on integrated graphics. With integrated you will not be able to play at mex settings/resolutions at good fps.

Id say get atleast a 6450 or better yet a 6570/6670.

If its just for minecraft and normal computer use 8gb of ram is useless. having more doesnt make it faster, having more then you will use just makes that much ram not being used. and ram unused is pointless. You can have 4gb and still not use all 4gb of it, even while gaming.

And unless you are going to be playing more demanding games, or doing lots of video recording/editing/rendering, there isnt much need for a quad core cpu, you would be fine with a 2nd gen core i3.

Minecraft is not a very graphics and CPU demanding game. That desktop will easily run the game.