Start-up development, success, and sustainability are affected by contextual factors that constitute a regional entrepreneurship ecosystem. Based on previous literature, we propose the conceptual framework Start-Up Ecosystem (StUpEco) that highlights the contextual drivers of a start-up business affected by the entrepreneurial ecosystem entities involved within the quadruple helix model. Furthermore, the proposed framework is tested according to the perceptions of Greek start-uppers through an empirical survey. According to our findings, the start-uppers’ motivation is explained mainly through opportunity rather than necessity. The study identifies government issues, such as tax incentives and acceleration of starting procedures, availability of funding opportunities, connectivity of stakeholders, entrepreneurship education, previous start-up experience, incubator support, as well as mentoring, as the most significant issues affecting the successful development of start-ups.