I want a rough estimate of the percentage of nouns that belongs to each gender category
According to a footnote in this study (Warning: PDF file):
which means you can roughly say that 40% are feminine, 40% are masculine and 20% are neuter
An interesting addendum (or extension to all words) to idober's answer:
If you assume that none of these three categories is favoured, and you look at the distribution of articles used, you get a similar result:
Now this is very rough, because you only take into account "der,die,das" while "die" is used in more feminine inflections than "der". There are more inaccuracies, but the rough picture is a nice estimate, I believe.
However, I find it interesting that you get a result that is very close to the study based on CELEX data.