The properties of the solar wind represent a mixture of indicators for solar origin and transport effects. Both are of interest for the understanding of heliophysics and space weather effects. Most available solar wind classifications focus on the solar origin, in part based on transport effected properties. We aim to identify the solar wind properties that are most important for solar wind classification. We select seven solar wind properties: proton density, proton speed, proton temperature, absolute magnetic field strength, proton-proton collisional age, the ratio between the densities of O6+ and O7+ and the mean charge state of Fe. We apply an unsupervised machine learning method, k-means, to each subset of the these parameters and compare the results to a reference case based on all seven solar wind properties. Two scenarios are considered which provide a simple and a detailed solar wind classification, respectively. We identified the proton density as the most important solar wind property for solar wind classification. Furthermore, we found that charge state composition is important to accurately identify the solar source region. This holds for the simple case of three solar wind types but is even more important for a more detailed classification. In comparison to proton density and proton temperature, the solar wind speed turns out to be a less influential property. Our results underscore the importance of highly accurate measurements, in particular for proton density, proton temperature and the charge state composition.