In this work, we present results for classification of different classes of targets (car, single and multiple people, bicycle) using automotive radar data and different neural networks. A fast implementation of radar algorithms for detection, tracking, and micro-Doppler extraction is proposed in conjunction with the automotive radar transceiver TEF810X and microcontroller unit SR32R274 manufactured by NXP Semiconductors. Three different types of neural networks are considered, namely a classic convolutional network, a residual network, and a combination of convolutional and recurrent network, for different classification problems across the 4 classes of targets recorded. Considerable accuracy (close to 100% in some cases) and low latency of the radar pre-processing prior to classification (approximately 0.55s to produce a 0.5s long spectrogram) are demonstrated in this paper, and possible shortcomings and outstanding issues are discussed.