I used to have a PC not too dissimilar to that. I suppose this PC should be OK for Minecraft game play, but recording not so much.
I would be worried about the power supply they may provide you with, though. This is usually one of the components sellers decide to cut back on. The PC may perform well with the current card and CPU etc. but when you begin to add upgrades you may begin to run into problems.
Personally, I would build a desktop myself so I know exactly what I'm buying and if it's decent or not.
