As the interest in deep learning tools continues to rise, new multimedia research fields begin to discover its potential. Both image and point cloud coding are good examples of technologies where deep learning-based solutions have recently displayed very competitive performance. In this context, this paper brings two novel contributions to the point cloud geometry coding state-of-the-art; first, a novel neighborhood adaptive distortion metric to be used in the training Loss function, which allows significantly improving the rate-distortion performance with commonly used objective quality metrics; second, an explicit quantization approach at the training and coding times to generate varying rate/quality with a single trained deep learning coding model, effectively reducing the training complexity and storage requirements. The result is an improved deep learning-based point cloud geometry coding solution, which is both more compression efficient and less demanding in training complexity and storage.