Student preference survey construction

I am reaching out to the community for ideas on how to construct a survey for student preference of research advisor. Here's the purpose. From a list of approx thirty professors, students need to rank their top five preferences of who they would like to work with on their research project. There would ideally be an option to input someone not on the list, but that could be a different question if necessary. The question then becomes how to fairly pair students and advisors based on their selections and if that can somehow be built into the survey. We prefer that priority not be first come, first serve, as in, the order in which respondents completed the survey, since there maybe accessibility issues that make that unfair. Our idea is to randomly select the priority order, which could be done outside of the survey, using a random number generator to assign an order, as in, respondent x was randomly assigned number 1, so they get their first preference, then respondent y was randomly assigned number 2, so they get their first preference, unless that was respondent x's first choice, then they get their second choice, and so on. If this could somehow be built into the survey, that would be ideal. Any ideas about how this could be constructed would be most appreciated, even if it's just the first part described above, the ranking part. If necessary, we can determine priority given the data after the survey.