Background: Precision medicine (PM) considers the genetic variability of individuals to identify tailored diagnosis and treatments. It relies on the possibility of gathering the widest possible health data and genetic information from individuals to obtain a broad pool of comparative data. To achieve this goal, the Region of Valle d’Aosta, since 2019, has co-financed the research center CMP³VdA, aiming to sequence 5000 genomes of patients with neurodevelopmental, neurodegenerative, oncological, and organ transplantation diseases, and to investigate the genetic variability of the resident population. Methods: This paper presents the results of an online survey of 472 (328F) respondents regarding willingness to participate in the genomic project and awareness, attitudes, and concerns about PM. Results: The main results show that the vast majority (92.6%) would be willing to participate—a higher percentage than in previous studies. Age, education, and prior experience in the healthcare sector are significant factors influencing the awareness of PM. Additionally, subgroups organized by age, gender, and religiosity show significant differences with respect to participants’ reasons for participating in research and which types of biological samples they would be willing to donate. Conclusions: Our findings can serve as a guide for stakeholders—particularly policymakers—to target institutional communication and achieve maximum participation in genomic research projects.