Two-dimensional semiconductors are excellent candidates for next-generation electronics and optoelec-tronics thanks to their electrical properties and strong light-matter interaction. To fabricate devices with optimal electrical properties, it is crucial to have both high-quality semiconducting crystals and ideal con-tacts at metal-semiconductor interfaces. Thanks to the mechanical exfoliation of van der Waals crystals, atomically-thin high-quality single-crystals can easily be obtained in a laboratory. However, conventional metal deposition techniques can introduce chemical disorder and metal-induced mid-gap states that induce Fermi level pinning and can degrade the metal-semiconductor interfaces, resulting in poorly performing devices. In this article, we explore the electrical contact characteristics of Au-InSe and graphite-InSe van der Waals contacts, obtained by stacking mechanically exfoliated InSe flakes onto pre-patterned Au or graphite electrodes without the need of lithography or metal deposition. The high quality of the metal-semiconductor interfaces obtained by van der Waals contact allows to fabricate high-quality Schottky di-odes based on the Au-InSe Schottky barrier. Our experimental observation indicates that the contact barrier at the graphite-InSe interface is negligible due to the similar electron affinity of InSe and graphite, while the Au-InSe interfaces are dominated by a large Schottky barrier.