I've built my own aero tank from an Ikea storage box and a 24V pond fogger. I started with these instructions and made a few tweaks and refinements over time, and the thing works quite well. Since there is no pump, and the fogger is perfectly quiet, all you can hear is a soft tinkling of water drops (the fogger knocks up a spray as well as fog). Add a grow lamp of your choosing (or sunlight), and done.
One thing I added was a styrofoam float to keep the fogger at ideal depth no matter the water level (which you can either make yourself or find on eBay).
The whole setup costs around £30 to build and has worked very well. The fogger lasts for about 6-9 months before it needs replacing (at about £12).