Any "rules of thumb" on number of features versus number of instances? (small data sets)
Multiple papers have opined that

only in rare cases is there a known distribution of the error as a function of the number of features and sample size.
The error surface for a given set of instances, and features, is a function of the correlation (or lack of) between features.

This paper suggests the following:

For uncorrelated features, the optimal feature size is $ N-1 $ (where $ N $ is sample size)
As feature correlation increases, and the optimal feature size becomes proportional to $ \sqrt N $ for highly correlated features.

Another (empirical) approach that could be taken, is to draw the learning curves for different sample sizes from the same dataset, and use that to predict classifier performance at different sample sizes. Here's the link to the paper.