To increase underwater acoustic signal detectability and conserve energy, nodes leverage directional transmissions. In addition, nodes operate in a three-dimensional (3D) environment that is categorized as inhomogeneous where a propagating signal changes its direction based on the observed sound speed profile (SSP). Coupling 3D directional transmission with frequent node drifts and the varying underwater SSP complicates the process of selecting suitable transmission angles to maintain underwater communication links. Fundamentally, utilizing directional transmission while nodes are drifting causes breaks in established communication links and thus nodes need to find new angles to reestablish these links. Moreover, selecting arbitrary transmission angles may lead to overlapping beams or result in leaving an underwater region uncovered. To tackle the abovementioned challenges, this paper proposes an autonomous beam selection approach that optimizes underwater communication by selecting non-overlapping beams while mitigating the possibility of missing a region, i.e., maximize coverage. Such optimization is achieved by utilizing a structured angle selection mechanism that accounts for the capability of the used transducer. Moreover, we introduce an algorithm suited for resource constrained nodes to classify rays into different types. Then we divide the underwater medium into regions where each region is identified by the limits of the coverage area of each ray type. Finally, we utilize the limits of these regions to aid nodes in selecting the best ray to reestablish communication with drifted nodes. We validate our contribution through simulation where actual SSPs are leveraged to validate the beam classification process.