I've been building quiet (not silent) computers for a very long time. I just checked my silentpcreview forum membership and I joined them more than 10 years ago.
What you want is really really difficult to achieve. A purely silent system with zero fans is practically impossible with anything more than mid level components. It will be stable at idle or desktop/office/web usage but it will overheat and throttle (or shutdown) if you actually stress it. If you go fanless you not only have to worry about your CPU and GPU temperatures, but you also have to worry about north/south bridge temperatures and memory and hard drive temperatures as well. Without airflow ambient temperatures start playing big role as well, if you're in basement where it's 66 degrees, it's one thing, if you're in a small room upstairs where it's 77 degrees, that can make enough difference to make your system unstable. When I was pushing the limits with just one 700rpm 120mm exhaust fan cooling my PC my northbridge was scorching hot to the touch, and my Crucial Ballistix DDR2 ram would start giving me random errors. Granted, that was the infamous ballistix RAM that was so prone to the failure and I still think it was colossal failure on the crucial part, but it didn't give me errors when I kept it cool, or at least not as many. Then you also have to keep in mind that many of the "fanless" parts such as fanless PSUs or fanless videocards rely on some redisual case airflow to cool them down. Most of those part will not work very well if there is zero airflow.
As I said, it is really really difficult to build a completely silent system. However, it is very easy to build almost silent one. Personally I find 120mm fans (Nexus Real Silent) under 700RPM to be practically inaudible. Technically it's not silent, but it is inaudible unless you're up at 2am at night with zero noise coming from elsewhere and unless you actually try to listen for it. A case with two 120mm 700RPM fans and fanless components is completely doable and will be practically inaudible for all intents and purposes. You will have to choose your components carefully, but it is possible and this is what I would recommend. One thing, once you go down that path, the choice of fans start to matter. There is not much difference between fans once you hit 1000+ RPMs because the wind noise drowns everything else, however at really slow speeds such as 700RPMs the wind noise goes away and fan bearing/motor becomes the dominant source of noise. From my experience I have found that Nexus Real Silent fan is really good for vertical mount (very poor for horizontal mount as it starts to click), and Scythe fans with Sony's FDB motors are really good for both vertical and horizontal mount. Also, keep in mind that noise and hearing is very subjective. I'm currently using Scythe GT fans on my videocard radiators because they're the best fans for radiators, however, in general I find their tonal qualities very annoying if running at full speeds, but to be honest I think I'm one of the very few people who thinks so, most people love GT's, so noise is subjective, you might have to try a few fans before you find the ones you like.
Anyway, good luck with your build.
If you prefer a more bling-y look, the same basic case is available with in a gamer style as the Raven RVZ-01.
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