The shift from private vehicles to public and shared transport is crucial to reducing emissions and meeting climate targets. Consequently, there is an urgent need to develop a multimodal transport trip planning approach that integrates public transport and shared mobility solutions, offering viable alternatives to private vehicle use. To this end, we propose a preference-based optimization framework for multi-modal trip planning with public transport, ride-pooling services, and shared micro-mobility fleets. We introduce a mixed-integer programming model that incorporates preferences into the objective function of the mathematical model. We present a meta-heuristic framework that incorporates a customized Adaptive Large Neighborhood Search algorithm and other tailored algorithms, to effectively manage dynamic requests through a rolling horizon approach. Numerical experiments are conducted using real transport network data in a suburban area of Rotterdam, the Netherlands. Model application results demonstrate that the proposed algorithm can efficiently obtain near-optimal solutions. Managerial insights are gained from comprehensive experiments that consider various passenger segments, costs of micro-mobility vehicles, and availability fluctuation of shared mobility.