In Faceted Search Systems (FSS), users navigate the information space through facets, which are attributes or meta-data that describe the underlying content of the collection. Type-based facets (aka t-facets) help explore the categories associated with the searched objects in structured information space. This work investigates how personalizing t-facet ranking can minimize user effort to reach the intended search target. We propose a lightweight personalisation method based on Vector Space Model (VSM) for ranking the t-facet hierarchy in two steps. The first step scores each individual leaf-node t-facet by computing the similarity between the t-facet BERT embedding and the user profile vector. In this model, the user's profile is expressed in a category space through vectors that capture the users' past preferences. In the second step, this score is used to re-order and select the sub-tree to present to the user. The final ranked tree reflects the t-facet relevance both to the query and the user profile. Through the use of embeddings, the proposed method effectively handles unseen facets without adding extra processing to the FSS. The effectiveness of the proposed approach is measured by the user effort required to retrieve the sought item when using the ranked facets. The approach outperformed existing personalization baselines.