Downscaling of the contact length Lc of a side-contacted carbon nanotube field-effect transistor (CNTFET) is challenging because of the rapidly increasing contact resistance as Lc falls below 20-50 nm. If in agreement with existing experimental results, theoretical work might answer the question, which metals yield the lowest CNT-metal contact resistance and what physical mechanisms govern the geometry dependence of the contact resistance. However, at the scale of 10 nm, parameter-free models of electron transport become computationally prohibitively expensive. In our work we used a dedicated combination of the Green function formalism and density functional theory to perform an overall ab initio simulation of extended CNT-metal contacts of an arbitrary length (including infinite), a previously not achievable level of simulations. We provide a systematic and comprehensive discussion of metal-CNT contact properties as a function of the metal type and the contact length. We have found and been able to explain very uncommon relations between chemical, physical and electrical properties observed in CNT-metal contacts. The calculated electrical characteristics are in reasonable quantitative agreement and exhibit similar trends as the latest experimental data in terms of: (i) contact resistance for Lc = ∞, (ii) scaling of contact resistance Rc(Lc); (iii) metal-defined polarity of a CNTFET. Our results can guide technology development and contact material selection for downscaling the length of side-contacts below 10 nm.