Deriving the actual multispectral data from the output of the acquisition system is a key problem in the field of multispectral imaging. Solving it requires a characterization method and the training set (if any) on which the method relies. In this paper we propose three novel approaches in selecting a training set to be used for the characterization of a multispectral acquisition system. The first approach, which we call the Hue Analysis Method, is based on colorimetric considerations; the second and third approaches, which we call the Camera Output Analysis Method and the Linear Distance Maximization Method respectively, are mainly based on algebraic and geometrical facts. In all three cases the selected training sets will have relatively low numerosity and broad applicability. We also test our three approaches, as well as an approach from another author and a random selection method, on the data obtained from a real acquisition. We then compare the reconstructed reflectances with the measurements obtained using a spectrophotometer. Our results indicate that all our methods can be substantial improvements compared to a random selection of the training set, and that the performances of the Linear Distance Maximization Method make it the best choice among all the methods tried for application in a general context.