It would only go a little over the budget so it should be okay.
Using a controller, would it make it a lot easier to connect them up if I were to purchase the extra fans? Also, the case comes with 2 120mm included, do you think they will be the same as the ones below?
2 x BitFenix Spectre PRO 140mm Fan - All Black £12.98 (£25.96)
1 x BitFenix Spectre Plain BLACK 120mm Fan £5.99
I'm thinking about adding some blue BitFenix LED's too, since my keyboard is black with blue backlights. Which out of the three sizes (20cm, 30cm, 50cm) do you think would be suitable?
Yes and yes. With fan controller will be much easier to control speed of the fans which in turn will affect noise levels Spectre are the fans that will be included in the case.
As for GPU I agree with Space Monkey the R9 290 would be a good choice.