Optimal investment in battery energy storage systems, taking into account degradation, sizing and control, is crucial for the deployment of battery storage, of which providing frequency control is one of the major applications. In this paper, we present a holistic, data-driven framework to determine the optimal investment, size and controller of a battery storage system providing frequency control. We optimised the controller towards minimum degradation and electricity costs over its lifetime, while ensuring the delivery of frequency control services compliant with regulatory requirements. We adopted a detailed battery model, considering the dynamics and degradation when exposed to actual frequency data. Further, we used a stochastic optimisation objective while constraining the probability on unavailability to deliver the frequency control service. Through a thorough analysis, we were able to decrease the amount of data needed and thereby decrease the execution time while keeping the approximation error within limits. Using the proposed framework, we performed a techno-economic analysis of a battery providing 1 MW capacity in the German primary frequency control market. Results showed that a battery rated at 1.6 MW, 1.6 MWh has the highest net present value, yet this configuration is only profitable if costs are low enough or in case future frequency control prices do not decline too much. It transpires that calendar ageing drives battery degradation, whereas cycle ageing has less impact.