In this study, we present a novel stochastic optimisation framework for the selection, sizing, and operation of photovoltaic systems combined with heating, cooling, and energy storage technologies in buildings. The framework integrates building energy modelling, technology cost and performance analysis, and energy system optimisation while addressing future uncertainties in technology and electricity prices. A bi-objective optimisation problem is developed to minimise both the expected total system cost and the variability of costs under uncertain inputs. The tool encompasses various photovoltaic technologies (polycrystalline, monocrystalline and monocrystalline with one-axis tracking), electric heat pumps (air-to-water, ground-to-water, and reversible air-to-air), and energy storage systems (battery and hot-water cylinder). Electricity, heating, and cooling requirements are obtained from a physics-based building model of a typical office and a residential building in Nicosia, Cyprus. Results of cost-effective technology portfolios show that replacing traditional systems with photovoltaic technologies, lithium-ion batteries, reversible air-to-air heat pumps, and air-to-water heat pumps can significantly reduce costs and emissions. Incorporating cost-variability minimisation into the objective function of the optimisation problem leads to a more diverse technology mix, enhancing energy independence and robustness at the expense of higher expected costs. A well-balanced bi–objective approach where both objectives are simultaneously optimised increases expected costs by 2–3% depending on the building type, while reducing the worst–case costs by 5% and narrowing the range of cost variability by up to 29%. The results demonstrate the significance of incorporating uncertainty into building energy system design optimisation.