Ciaran92, here is something similar to your build but with some improvements:
If you have the cash later on you can add in a 120GB MX100 Crucial SSD, which will cost about £50 but you can use it to put the OS on, and a few games and programs, it will make your PC turn on MUCH faster, and anything you put on the SSD will start & load much quicker.
Also, if you can stretch your budget about £10 more, a FX 6300 is a good upgrade to the FX 4300, it's simply the same CPU but with 6 cores rather than 4 (and a slightly lower clockspeed).
This PC will be able to destroy minecraft, and will perform pretty well in most games. Of course it will struggle with AAA games such as Crysis 3 and Battlefield 4, but I assume you won't be playing those since you didn't mention it and it isn't really possible to get high settings on them with your current budget.
Multitasking will be a breeze with 4 cores (6 cores if you take the FX 6300 CPU), and 4GB of RAM is more than enough for your needs.
The R7 265 card is very powerful for games like Minecraft.
The case is one that I prefer over the one that you picked, however either should work so pick whichever you want.
The 500W EVGA PSU will last for a long time, and gives you enough room for future upgrades.
The fast 7200RPM hard drive will increase the speed that your PC boots up, and also increase the speed of loading things and starting programs.
Adding the SSD will make the PC even faster, but you will still be fine without it.
PCPartPicker part list /
Price breakdown by merchant
CPU: AMD FX-4300 3.8GHz Quad-Core Processor (£62.99 @ Amazon UK)
CPU Cooler: Cooler Master Hyper TX3 54.8 CFM Sleeve Bearing CPU Cooler (£23.50 @ Amazon UK)
Motherboard: ASRock 980DE3/U3S3 ATX AM3+ Motherboard (£41.06 @ Amazon UK)
Memory: Crucial 4GB (2 x 2GB) DDR3-1333 Memory (£31.99 @ Amazon UK)
Storage: Western Digital RE3 1TB 3.5" 7200RPM Internal Hard Drive (£33.99 @ Amazon UK)
Video Card: Sapphire Radeon R7 265 2GB Video Card (£89.99 @ Aria PC)
Case: Corsair SPEC-01 RED ATX Mid Tower Case (£37.99 @ Scan.co.uk)
Power Supply: EVGA 500W 80+ Certified ATX Power Supply (£29.40 @ Scan.co.uk)
Optical Drive: Samsung SH-224DB/BEBE DVD/CD Writer (£11.32 @ CCL Computers)
Total: £362.23
Prices include shipping, taxes, and discounts when available
Feel free to ask any questions you have about the build!