Grid-scale energy storage units are regarded as an enabler of the renewable-dominant power systems. Currently available energy storage technologies are ubiquitous, but not equally suitable for providing different grid support services. As part of their investment process, merchant energy storage investors need to ensure that their energy storage investments are well aligned with unique grid support needs of each power system and that the storage characteristics are suitable for the simultaneous provision of multiple services. This paper presents a model to optimize merchant investments in energy storage units that can compete in the joint energy and reserve market. The proposed model uses the bilevel programming framework to maximize the expected lifetime profit and to ensure a desirable rate-of-return for the merchant energy storage investor, while endogenously considering market clearing decisions over a set of characteristic days. The bilevel model is first converted into a single-level equivalent using the Karush-Kuhn-Tucker-based approach and then linearized to obtain a mixed-integer linear program. The resulting program is solved using the Benders' decomposition approach and tested on the 8-zone Independent System Operator New England test system. The case study provides numerical insights that are discussed from viewpoints of the merchant energy storage owner, the system operator, and the regulator.