I'd recommend assessing the performance of the model "as-is" and then decide for feature selection or not.
If you have good performance for both train / test sets, then there's no need to perform feature selection.
If you end up overfitting your data (low train error, high test error) you may want to reduce the number of features using feature selection / regularization (the cost function is penalized when the model uses a large number of parameters)
If you have low train performance, this means that you have high bias (the model does not learn properly from those features). This usually happens if the model is not complex enough to extract structure from the data. You may want to add features in this case, rather than selecting them out.
Hope this helps.