Audio ADCs are usually quite cheap, because of high volume production. So you get 2 or 4 channel version in the $1-$4 range. They usually come as 16 Bit (or more) and something like 48 kHz, but many can run slower as well.
Most of them are sigma delta, and as quality is not that important, I would not care about idle tones - this might be a thing of high end audio speculations. A nice thing about sigma delta converters is, that they simplify (nearly eliminate) the anti-aliasing filter a lot - this alone is an important point if you want low cost. Besides audio there are some cheap ADCs made for mains power measurement (e.g. MCP39xx).
If 12 Bits is good enough, one could in principle use µC internal converters (e.g. ARM M3 based). But the need for AA filtering might be the problem. So even with sampling at 40 kHz (to easy on AA) one could get something like 16 channels from a single chip.
With the 32 Channels, an important question is, if the all channels are needed active at the same. Also the interfacing circuit might be important. More channels in one chip might help here to keep the interface simpler.