From previous experience, the True Power Antec systems are the quietest. This appears to be a Smart Power system, which does (I believe) have the thermal sensing power leads for fans. My personal experience has been the volumes are about the same, but the the True Power seems to be a little quieter.
My recomendation is to go with that case, but plan on replacing the noisy Antec case fans (they are relatively quiet, but there are much quieter on the market) and buy some of the neon LED fans from CoolerMaster (your choice of color they all blow the same). These are some of the quietest fans (25dba) for the highest volume of air moved (32.11 CFM) - for the cheapest price ($7.99 - they go on sell sometimes for less - they used to only be $5.99). Plus they give you the cool geek light up factor that everyone seems to be so fond of.
These will quiet the case - now the only other source is the CPU heatsink. I would recommend buying the highest copper content heatsink (one of the Termalright SLK series) that your budget will allow, and that your MB will fit, and consider attaching one of the above fans. Depending on your desire to overclock (which if sound is your goal, I assume overclocking is not) you may need to sacrifice some sound level for higher CFM.
I have built only one 2500+ Barton with this setup (except that I think I left the stock AMD fan and cooler in), and it worked quite well. I have had no issues as of yet. Once the computer was put under the desk, the only indication that it was on was the blue fan light comming out from under the desk.
Just a rule of thumb, I have heard that anything less 30DB is barely audible on fans. I try to stick with this, and it has served me quite well. Just be sure to watch your CFM rates on low noise fans.