CHDK on Canon Powershot S100: Is there a Video Bitrate sweet spot?
No, there is no sweet spot for compression, whether it is on a camera or in encoding after the fact.  The needed data rate depends heavily on the content being recorded and is a complex field, though the best bet to handle it simply is to try adjusting it and decide when it works for your needs.  You can eventually get an idea of the quality from each bitrate for your camera, but we can't really give you guidelines as both noise level and the particular encoder used by your camera will also impact the way things turn out.

One important caveat to keep in mind when dealing with compression on a camera is that if you are going to edit the footage, you want to make sure you use a high enough quality that re-compressing after editing does not result in quality loss either.  With lossy compression, each additional compression results in further quality loss and a video that looks fine initially may fall apart when compressed for final output.  The larger your source videos are, the smaller you are likely to be able to compress your final video to.  You may also want to shoot All-I if it is an option because this format is far more efficient in editing software than compressions that are group of picture based (IPB), though they also take far more space to get good quality.

Also, you say that 14MBps is obviously too high, but I would challenge you that it is not obviously too high.  Uncompressed, 1080p video at 24fps would still take 150MBps or 1194mbps.  You are still compressing over 90% at 14MBps.  Bluray will often use in the neighborhood of 35 to 50mbps which is still up to almost half of the 112mbps data rate you quoted as the max.  Particularly if that is All-I, 112mbps is not an unexpectedly high value at all.