Context: The quality of the test suites and the constituent test cases significantly impacts confidence in software testing. While research has identified several quality attributes of test cases and test suites, there is a need for a better understanding of their relative importance in practice. Objective: We investigate practitioners' perceptions regarding the relative importance of quality attributes of test cases and test suites and the challenges they face in ensuring the perceived important quality attributes. Method: We conducted an industrial survey using a questionnaire based on the quality attributes identified in an extensive literature review. We used a sampling strategy that leverages LinkedIn to draw a large and heterogeneous sample of professionals with experience in software testing. Results: We collected 354 responses from practitioners with a wide range of experience. We found that the majority of practitioners rated Fault Detection, Usability, Maintainability, Reliability, and Coverage to be the most important quality attributes. Resource Efficiency, Reusability, and Simplicity received the most divergent opinions, which, according to our analysis, depend on the software-testing contexts. We identified common challenges that apply to the important attributes, namely inadequate definition, lack of useful metrics, lack of an established review process, and lack of external support. Conclusion: The findings point out where practitioners actually need further support with respect to achieving high-quality test cases and test suites under different software testing contexts. The findings can serve as a guideline for academic researchers when looking for research directions on the topic. The findings can also be used to encourage companies to provide more support to practitioners to achieve high-quality test cases and test suites.