There is not a rule for choosing a feature selection algorithm: it depends on the dataset under study. There are filter and wrapper based approaches for performing feature selection. Given that wrapper procedures are bases in the obtained performances of the learner on each feature subspace, they gives better results than filter methods which are independent of the prediction model.
Note that PCA and LDA are feature transformation methods (not feature selection).
There is not a rule for choosing a feature selection algorithm: it depends on the dataset under study. There are filter and wrapper based approaches for performing feature selection. Given that wrapper procedures are bases in the obtained performances of the learner on each feature subspace, they gives better results than filter methods which are independent of the prediction model.
Note that PCA and LDA are feature transformation methods (not feature selection).
No more to add than Pedro a part of the link to the wiki which give more detailed information on the methods themselves.
http://en.wikipedia.org/wiki/Feature_selection
Given that your dataset is small, then you will not have much penalty in using wrapper techniques, since each run would be computationally relatively cheap. As for what kind of search algorithm you should use in the space of the feature subsets there is no clear answer. Both forward selection and backward elimination will work ok. If the number of features is quite large, then GAs might be better at finding the global optimal subset. In any case, I would base the evaluation function (scoring metric for a specific feature subset) on some form of cross validation.
On a small dataset, I would suggest to use all-subset procedure. You can find it in QSARINS software (http://www.qsar.it/)
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