If you could suggest me some cute-good looking cases to fit my build in : http://pcpartpicker.com/p/cWQwkL it would be great. I don't want anything white. Thanks.
And btw if you can confirm whether all my parts are compatible or not, it would be cute.
Micro ATX and £40 budget, can't see you getting anything better then a USB3 variant of the Fractal Design Core 1000, unless you find a Arc Mini R2 on sale.
not sure i can help you choose a case (the new Corsair Air 240 looks AWESOME.... might make me go from ATX to M-ATX....) HOWEVER, i couple suggestions.
why the 2133Mhz RAM? get a nice 1600 kit.
and i would opt for a WD HDD. WD 1TB blue (seagate have high failure rates).
A very cheap but very solid, well finished, and well engineered case for µATX is the Antec DSK3000B (http://www.antec.com/product.php?id=706755&fid=5022056).
It's Intel TAC 2.0 certified (http://cache-www.intel.com/cd/00/00/38/71/387155_387155.pdf), so it's got adequate airflow even with it's smaller 92mm fans, which offer the benefit of more room inside despite the small dimensions of the case, and it's got a timeless modern functional design, and it only costs 30 EUR.
Everyone with an Antec case will tell you that they last a really long time and stay goodlooking. It's like CaseLabs cases, they have a huge brand customer fidelity because of the quality. I still use Antec NineHundred cases for a lot of systems, that have had their 4th complete system rebuild since they were bought, and that's for intensive commercial use and they've been moved a lot, and they still look like new after 10 years or so. Even the exact same fans (Antec Tri-Cool fans) can still be bought for a very reasonable price from Antec if the fans are used up, but I haven't had to swap out the fans on all of these systems after 24/7 operation for 10 years, and that's with thermally loaded systems with 6-8 high speed hard drives in them and dual graphics cards or a high performance graphics card and a RAID card, so these things get really hot.
There's more fancy or blingy available out there, but it's going to be very hard to find better quality where it counts and better price/performance than Antec cases.
It's a waste of money in this system build unless it's less than like 15 bucks for 2133 over 1600, you could spend the extra dollars on something else :)