In a faceted search system, type-based facets (t-facets) represent the categories of the resources being searched. Ranking algorithms are needed to select and promote the most relevant t-facets. However, as these are extracted from large multi-level taxonomies, they are impossible to show entirely to the user. Facet ranking is usually employed to filter out irrelevant facets for the users. Existing facet ranking methods neglect both the hierarchical structure of t-facets and the user historical preferences. This research introduces a personalized t-facet ranking that addresses both issues. During a first step, a Deep Neural Network (DNN) model is trained to assign a relevance score to each t-facet based on three groups of relevance features. The score reflects the t-facet relevance to the user, the input query, and its general importance in the dataset. Subsequently, these scores are aggregated and the t-facets are re-organised into a smaller sub-tree to be presented to the user. Our approach aims at minimizing the effort required by the user to reach their intended search target. This is measured in terms of number of clicks the user has to perform on the t-facet tree to reach a relevant resource. The approach is applied to a Point-Of-Interest suggestion task. We solve the problem by ranking the categories of the venues as t-facets. The evaluation compares our DNN-based approach with other existing baselines and investigates the individual contribution of each group of features. Our experiment has demonstrated that the proposed personalized deep learning model leads to better t-facet rankings and minimized user effort.