GPU: I don't know of any screens with a 2560x1900 solution. Do you mean 2560x1440? or 2560x1600? Look for a passively cooled radeon 7750. What games do you intend to play and at what resolution and graphical settings?
Mobo: I prefer ASUS boards because of their windows application, FanXpert. It's a great, simple application that'll allow you to easily control the CPU fan and the case fans (though the number of case fans supported is usually limited).
Case: Since you've looked at the Corsair cases I assume that you are looking at ATX cases. In that case, have a look at the following cases:
NZXT Source 210 Elite
NZXT Source 220
Fractal Design R4
Fractal Design Arc Midi
Fractal Design Core 3000
You could also consider a m-ATX system. In which case, you could look for the Silverstone Temjin TJ08-e and the Silverstone Precision PS07.
PSU: 400 W is definitely enough for a i5 3350p and a Radeon 7750. Since you want a fanless PSU, have a look at the Seasonic X400. It can easily handle the CPU and GPU mentioned. If you're ok with a "fanned" PSU then have a look at the Seasonic G360 which runs very quietly. It's much cheaper and even earned an Editor's Choice here at SPCR.http://www.silentpcreview.com/article1297-page5.html
The only drawback is that it isn't modular.
CPU cooler: Your CPU only has a TDP at 69 W. That's not much. Must people would probably recommend a Cooler Master Hyper 212 EVO + a good PWM fan. But you could save some money by going with a Scythe Katana 3. Though it doesn't have the same cooling performance as the Hyper 212 EVO, it can easily cope with the 3350p quietly. Simple have a look at this review where the temperature of the 95 W CPU used only rises 26 C when the fan is run at an inaudible speed.