tomc856 :
My budget is probably anything up to around £200, and I intend to play games like The Crew, Stranded Deep, Arma 2 and Rust.
In my opinion, I think you'd be better off sending that PC back to them and building one, there are some already great guide here for it, and we can suggest you some to fit your budget.
If that is not an option, we should be able to sort you out with something. Your motherboard socket is only FM2, which restricts potential upgrades, it'd definitely be beneficial having a FM2+ or even the FM3 socket now but that means a motherboard upgrade would also be required. Considering your current CPU is dual core, you'll see benefit from a CPU upgrade as well as a GPU upgrade. For the FM2 socket I'd take a look at the A10 series. I know you'd like an AMD GPU too, but its probably more advisable to go for an Nvidia GPU, as your case likely has poor cooling efficiency and Nvidia GPUs run a lot cooler than AMD ones which will keep your overall temps down.
I'd highly suggest looking at these parts for an upgrade.
PCPartPicker part list:
http://uk.pcpartpicker.com/p/QDtwYJ
Price breakdown by merchant: http://uk.pcpartpicker.com/p/QDtwYJ/by_merchant/
CPU: AMD A10-6800K 4.1GHz Quad-Core Processor (£92.80 @ Aria PC)
Video Card: Gigabyte GeForce GTX 750 Ti 2GB WINDFORCE Video Card (£108.96 @ Amazon UK)
Total: £201.76
Prices include shipping, taxes, and discounts when available
Generated by PCPartPicker 2015-05-05 04:22 BST+0100