As the number of Cloud services is growing at a tremendous speed, there is an increasing number of service providers offering similar functionalities. Selecting services with user desired non-functional properties (NFPs) becomes of significant importance but triggers a number of Big Data related research issues. First, the selection decision should deal with a large volume of service NFPs data. Second, service selection needs to reflect diverse user preferences, including both qualitative and quantitative ones. Third, the uncertainty of the network and service load leads to high variability in NFPs. Fourth, as the trust values of service NFPs are collected via historic user's feedbacks, it brings the veracity dimension to the NFPs of services. Fifth, multiple and sometimes conflicting decision objectives for optimal service selection should be balanced. An effective service selection mechanism is in demand that can tackle all the above Big Data challenges in an integrated way to handle the highly diverse QoS with significant variability along with the trust related issues giving rise to data veracity. Existing investigations focus on either users' QoS preferences or their trust concerns but fail to provide a systematic solution to integrate both criteria in the selection process. In this paper, we tackle heterogeneous preferenceand trust-based service selection by developing a novel multi-objective optimization approach to make trade-off decision between service's trust value and user's QoS preference to rank candidate Cloud services based on their match degrees with users' requirements. We conduct extensive experiments to evaluate the effectiveness and efficiency of the proposed approach.