Molecular line emission is a powerful probe of the physical conditions of astrophysical objects but can be complex to model, and it is often unclear which transitions would be the best targets for observers who wish to constrain a given parameter. We therefore produce a list of molecular species for which the gas history can be ignored, removing a major modelling complexity. We then determine the best of these species to observe when attempting to constrain various physical parameters. To achieve this, we use a large set of chemical models with different chemical histories to determine which species have abundances at 1 MYr that are insensitive to the initial conditions. We then use radiative transfer modelling to produce the intensity of every transition of these molecules. We finally compute the mutual information between the physical parameters and all transitions and transition ratios in order to rank their usefulness in determining the value of a given parameter. We find 48 species that are insensitive to the chemical history of the gas, 23 of which have collisional data available. We produce a ranked list of all the transitions and ratios of these species using their mutual information with various gas properties. We show mutual information is an adequate measure of how well a transition can constrain a physical parameter by recovering known probes and demonstrating that random forest regression models become more accurate predictors when high-scoring features are included. Therefore, this list can be used to select target transitions for observations in order to maximize knowledge about those physical parameters
