Recent technology development of logic devices based on 2-D semiconductors such as MoS2, WS2, and WSe2 has triggered great excitement, paving the way to practical applications. Making low-resistance p-type contacts to 2-D semiconductors remains a critical challenge. The key to addressing this challenge is to find high-work function metallic materials which also introduce minimal metal-induced gap states (MIGSs) at the metal/semiconductor interface. In this work, we perform a systematic computational screening of novel metallic materials and their heterojunctions with monolayer WSe2 based on ab initio density functional theory and quantum device simulations. Two contact strategies, van der Waals (vdW) metallic contact and bulk semimetallic contact, are identified as promising solutions to achieving Schottky-barrier-free and low-contact-resistance p-type contacts for WSe2 p-type field-effect transistor (pFETs). Good candidates of p-type contact materials are found based on our screening criteria, including 1H-NbS2, 1H-TaS2, and 1T-TiS2 in the vdW metal category, as well as Co3Sn2S2 and TaP in the bulk semimetal category. Simulations of these new p-type contact materials suggest reduced MIGS, less Fermi-level pinning effect, negligible Schottky barrier height and small contact resistance (down to Formula Omitted).