There are a large number of time domain, frequency domain and time-frequency signal processing methods available for univariate feature extraction. However, there is no consensus in SHM on which feature, or feature sets, are best suited for the identification, localisation and prognosis of damage. This paper attempts to address this problem by providing a comprehensive benchmark of feature selection & reduction methods applied to an extensive set of univariate features. These univariate features are extracted using multiple statistical, temporal and spectral methods from the benchmark S101 and Z24 bridge datasets. These datasets contain labelled accelerometer recordings from full scale bridges as they are progressively subjected to multiple damage scenarios. To identify the minimal set of features that best distinguishes between the multiple damage states, a supervised machine learning approach is used in combination with multiple feature selection methods. The ability of these reduced feature sets to distinguish between damage states is benchmarked using the prediction performance of the classification models, with the training and test sets obtained through stratified k-fold cross validation. The results obtained show that reduced sets of univariate features, extracted from a single accelerometer sensor, are capable of accurately distinguishing between multiple classes of healthy and damaged states. This work provides a benchmark for SHM practitioners and researchers alike for the choice, comparison and validation of feature extraction and feature selection methods across a wide range of systems.