Abnormalities and defects that can cause lumbar spinal stenosis often occur in the Intervertebral Disc (IVD) of the patient's lumbar spine. Their automatic detection and classification require an application of an image analysis algorithm on suitable images, such as mid-sagittal images or traverse mid-height intervertebral disc slices, as inputs. Hence the process of selecting and separating these images from other medical images in the patient's set of scans is necessary. However, the technological progress in making this process automated is still lagging behind other areas in medical image classification research. In this paper, we report the result of our investigation on the suitability and performance of different approaches of machine learning to automatically select the best traverse plane that cuts closest to the half-height of an IVD from a database of lumbar spine MRI images. This study considers images features extracted using eleven different pre-trained Deep Convolution Neural Network (DCNN) models. We investigate the effectiveness of three dimensionality-reduction techniques and three feature-selection techniques on the classification performance. We also investigate the performance of five different Machine Learning (ML) algorithms and three Fully Connected (FC) neural network learning optimizers which are used to train an image classifier with hyperparameter optimization using a wide range of hyperparameter options and values. The different combinations of methods are tested on a publicly available lumbar spine MRI dataset consisting of MRI studies of 515 patients with symptomatic back pain. Our experiment shows that applying the Support Vector Machine algorithm with a short Gaussian kernel on full-length image features extracted using a pre-trained DenseNet201 model is the best approach to use. This approach gives the minimum per-class classification performance of around 0.88 when measured using the precision and recall metrics. The median performance measured using the precision metric ranges from 0.95 to 0.99 whereas that using the recall metric ranges from 0.93 to 1.0. When only considering the L3/L4, L4/L5, and L5/S1 classes, the minimum F1-Scores range between 0.93 to 0.95, whereas the median F1-Scores range between 0.97 to 0.99.