Future autonomous transportation is one of the most demanding application areas in terms of connectivity, as it has to simultaneously meet stringent criteria that do not typically go hand in hand, such as high throughput, low latency, high coverage/availability, high positioning and sensing accuracies, high security and robustness to interferences, etc. In order to meet the future demands of challenging applications, such as applications relying on autonomous vehicles, terrestrial networks are no longer sufficient and are to be augmented in the future with satellite-based networks. Among the emerging satellite networks, Low Earth Orbit (LEO) networks are able to provide advantages over traditional Medium Earth Orbit (MEO) and Geo-Stationary Earth Orbit (GEO) networks in terms of signal latency, cost, and performance. Nevertheless, several challenges exist in LEO system design, which have not been fully addressed in the existing literature. In particular, the problem of LEO-system optimization of design parameters is a multi-dimensional problem with many aspects to be considered. This paper offers a comprehensive survey of the LEO-system design parameters, of the challenges in LEO system design process, and of the optimization methods for satellite communication, positioning, and sensing applications, as well as a summarizing discussion on the design considerations for LEO-based networks to support future autonomous transportation.