There is nothing wrong with an FX6300, but if you wanted to I'm fairly confident you could go with an FX8320/8350 or an Intel i5 build if that was preferable.
Everything is pretty sensible. I'd change the HDD, as you can pick up a 1TB Caviar Blue or 1TB Barracuda for under £60, which is far better value.
Assuming you are looking at graphics cards in the ~£200 range, and cases in the ~£50 range...
In video cards I'd say you are looking at the GTX760, R9 280X or HD7970. The GTX760 is the cheapest (£180+) but weakest of the three. If you have a preference towards Nvidia then its pretty much the only thing in that vicinity. The 280X and HD7970 are very similar products, but as the HD7970 is being phased out you'll probably see decent offers on them. The 280X starts at around £230, most HD7970s will be similarly priced though you'll see the odd one drop nearer to £200.
Cases are fairly subjective, people pick them on aesthetics, but have a look at the Corsair 200R, Bitfenix Shinobi, NZXT Source 210, Antec Three Hundred Two or Fractal Design Core 3000 for quality cheaper cases. See if any of those interest you