When developing and analyzing new hyperparameter optimization methods, it is vital to empirically evaluate and compare them on well-curated benchmark suites. In this work, we propose a new set of challenging and relevant benchmark problems motivated by desirable properties and requirements for such benchmarks. Our new surrogate-based benchmark collection consists of 14 scenarios that in total constitute over 700 multi-fidelity hyperparameter optimization problems, which all enable multi-objective hyperparameter optimization. Furthermore, we empirically compare surrogate-based benchmarks to the more widely-used tabular benchmarks, and demonstrate that the latter may produce unfaithful results regarding the performance ranking of HPO methods. We examine and compare our benchmark collection with respect to defined requirements and propose a single-objective as well as a multi-objective benchmark suite on which we compare 7 single-objective and 7 multi-objective optimizers in a benchmark experiment. Our software is available at [https://github.com/slds-lmu/yahpo_gym].