Document clustering is frequently used in applications of natural language processing, e.g. to classify news articles or create topic models. In this paper, we study document clustering with the common clustering pipeline that includes vectorization with BERT or Doc2Vec, dimension reduction with PCA or UMAP, and clustering with K-Means or HDBSCAN. We discuss the inter- actions of the different components in the pipeline, parameter settings, and how to determine an appropriate number of dimensions. The results suggest that BERT embeddings combined with UMAP dimension reduction to no less than 15 dimensions provides a good basis for clustering, regardless of the specific clustering algorithm used. Moreover, while UMAP performed better than PCA in our experiments, tuning the UMAP settings showed little impact on the overall performance. Hence, we recommend configuring UMAP so as to optimize its time efficiency. According to our topic model evaluation, the combination of BERT and UMAP, also used in BERTopic, performs best. A topic model based on this pipeline typically benefits from a large number of clusters.