Comet Interceptor is an ESA science mission with payload contributions from ESA Member States and with an international participation by JAXA. It is the first mission that is being designed, built, and potentially launched before its target is known. This approach will enable the spacecraft to perform the first mission to a Long Period Comet from the Oort Cloud, as these comets have fleeting visits to the inner Solar System lasting only months to years from first discovery, too short for the usual process of mission development to be followed. In this paper we describe a number of factors that need to be considered in selecting a target for the mission, including scientific, orbital, spacecraft and instrument constraints, and discussion of different prioritisation strategies. We find that, in the case where we have a choice of targets, our decisions will mostly be driven by orbital information, which we will have relatively early on, with information on the activity level of the comet an important but secondary consideration. As cometary activity levels are notoriously hard to predict based on early observations alone, this prioritisation / decision approach based more on orbits gives us confidence that a good comet that is compatible with the spacecraft constraints will be selectable with sufficient warning time to allow the mission to intercept it.