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This paper studies the indoor localisation of WiFi devices based on a commodity chipset and standard channel sounding. First, we present a novel shallow neural network (SNN) in which features are extracted from the channel state information (CSI) corresponding to WiFi subcarriers received on different antennas and used to train the model. The single-layer architecture of this localisation neural network makes it lightweight and easy-to-deploy on devices with stringent constraints on computational resources. We further investigate for localisation the use of deep learning models and design novel architectures for convolutional neural network (CNN) and long-short term memory (LSTM). We extensively evaluate these localisation algorithms for continuous tracking in indoor environments. Experimental results prove that even an SNN model, after a careful handcrafted feature extraction, can achieve accurate localisation. Meanwhile, using a well-organised architecture, the neural network models can be trained directly with raw data from the CSI and localisation features can be automatically extracted to achieve accurate position estimates. We also found that the performance of neural network-based methods are directly affected by the number of anchor access points (APs) regardless of their structure. With three APs, all neural network models proposed in this paper can obtain localisation accuracy of around 0.5 metres. In addition the proposed deep NN architecture reduces the data pre-processing time by 6.5 hours compared with a shallow NN using the data collected in our testbed. In the deployment phase, the inference time is also significantly reduced to 0.1 ms per sample. We also demonstrate the generalisation capability of the proposed method by evaluating models using different target movement characteristics to the ones in which they were trained.