I have a bunch of sets of data (between 50 to 500 points, each of which can take a positive integral value) and need to determine which distribution best describes them. I have done this manually for several of them, but need to automate this going forward.

Some of the sets are completely modal (every datum has the value of 15), some are strongly modal or bimodal, some are bell-curves (often skewed and with differing degrees of kertosis/pointiness), some are roughly flat, and there are any number of other possible distributions (possion, power-law, etc.). I need a way to determine which distribution best describes the data and (ideally) also provides me with a fitness metric so that I know how confident I am in the analysis.

Existing open-source libraries would be ideal, followed by well documented algorithms that I can implement myself.