You wouldn't necessarily have to change your feature selection method (though you may want to depending on the question you're asking). You should change the way your target classes are represented though, if you're using machine learning classifiers.
Continuous variables can be predicted by regression, as you stated. Discrete variables can also be done in this way if you don't care about strict boundaries between classes (e.g. 2.5 is an acceptable answer), but if you're looking for a potentially more accurate output, you could use indicator variables to create a separate classification boundary.
So let's say you had age classes 1, 2, and 3. You would create the target label matrix of dimension M, where M = # of instances you wish to classify:
[ [ 1 0 0 ],
[ 0 1 0 ],
[ 0 0 1 ],
[ 0 1 0 ],
[ 1 0 0 ] ]
Each column represents a true/false value for each age category. This way, feature selection won't select features as often that correspond to an output of age class 2.5, but will instead favor outputs that correctly classify to age class 2 or 3.
All of this depends on which feature selection strategy you use though.