Time-Frequency Distributions (TFDs) support the heart sound characterisation and classification in early cardiac screening. However, despite the frequent use of TFDs in signal analysis, no study comprehensively compared their performances on deep learning for automatic diagnosis. Furthermore, the combination of signal processing methods as inputs for Convolutional Neural Networks (CNNs) has been proved as a practical approach to increasing signal classification performance. Therefore, this study aimed to investigate the optimal use of TFD/ combined TFDs as input for CNNs. The presented results revealed that: 1) The transformation of the heart sound signal into the TF domain achieves higher classification performance than using of raw signals. Among the TFDs, the difference in the performance was slight for all the CNN models (within $1.3\%$ in average accuracy). However, Continuous wavelet transform (CWT) and Chirplet transform (CT) outperformed the rest. 2) The appropriate increase of the CNN capacity and architecture optimisation can improve the performance, while the network architecture should not be overly complicated. Based on the ResNet or SEResNet family results, the increase in the number of parameters and the depth of the structure do not improve the performance apparently. 3) Combining TFDs as CNN inputs did not significantly improve the classification results. The findings of this study provided the knowledge for selecting TFDs as CNN input and designing CNN architecture for heart sound classification.