Formation of low-resistance metal contacts is the biggest challenge that masks the intrinsic exceptional electronic properties of two dimensional WSe2 devices. We present the first comparative study of the interfacial properties between monolayer/bilayer (ML/BL) WSe2 and Sc, Al, Ag, Au, Pd, and Pt contacts by using ab initio energy band calculations with inclusion of the spin-orbital coupling (SOC) effects and quantum transport simulations. The interlayer coupling tends to reduce both the electron and hole Schottky barrier heights (SBHs) and alters the polarity for the WSe2-Au contact, while the SOC chiefly reduces the hole SBH. In the absence of the SOC, the Pd contact has the smallest hole SBH. Dramatically, the Pt contact surpasses the Pd contact and becomes the p-type ohmic or quasi-ohmic contact with inclusion of the SOC. Therefore, p-type ohmic or quasi-ohmic contact exists in WSe2-metal interfaces. Our study provides a theoretical foundation for the selection of favorable metal electrodes in ML/BL WSe2 devices.