Node connectivity plays a central role in temporal network analysis. We provide a comprehensive study of various concepts of walks in temporal graphs, that is, graphs with fixed vertex sets but edge sets changing over time. Importantly, the temporal aspect results in a rich set of optimization criteria for "shortest" walks. Extending and significantly broadening state-of-the-art work of Wu et al. [IEEE TKDE 2016], we provide a quasi-linear-time algorithm for shortest walk computation that is capable to deal with various optimization criteria and any linear combination of these. A central distinguishing factor to Wu et al.'s work is that our model allows to, motivated by real-world applications, respect waiting-time constraints for vertices, that is, the minimum and maximum waiting time allowed in intermediate vertices of a walk. Moreover, other than Wu et al. our algorithm does not request a strictly increasing time evolvement of the walk and can optimize a richer set of optimization criteria. Our experimental studies indicate that our richer modeling can be achieved without significantly worsening the running time.