I personally think this is a poor idea. If you know that your data comes from a certain distribution, you can probably say something meaningful. You may have 0/1 responses, so the distribution is binomial, may be conditional on some other covariates -- that's a logistic regression. You may have counts, so the distribution is Poisson, may be conditional on some other covariates -- that's Poisson or zero inflated Poisson or negative binomial regression. However, generally just peeking and the data and trying to determine the distribution rarely leads to good results.
Telling us what your ultimate goal of analysis is may help suggesting some better routes. Do you want to simulate new data from a similar distribution? Do you want to provide an analytical summary that's easy to compute for certain distributions? (I've seen people fit lognormal curve to income data, so as to report the Gini coefficient.) Do you want to compare your results with somebody else's?
Also, keep in mind that a small sample (say under 100) will be compatible with many possible distributions. A distribution with positive values only could be represented by a gamma, or a lognormal, or a beta, or by Pearson family, and there is simply no way distinguishing between them on the basis of the data only. On the other hand, large samples (say more than 10000) won't be compatible with anything, since the real life is richer than the assumptions we make about it.