Icons are useful in situations where you have limited space to present your interface. The increasing prevalence of Mobile development has caused a resurgence of interest in Icon based interfaces.
If your users will be using a mobile and desktop interface for the same site often, then it may be advisable to use icons in both, to unify the interface they utilize. This is what Google did with the new Gmail interface; they reduced the quality of the desktop UI a bit as a compromise to unify the design between their desktop and mobile platforms.
But without that need, there is little reason to use icon-only interfaces. With only three selections I see no reason to limit your space and provide only icons to the users. Larger click targets are faster to acquire anyway.