How to do physics in three.js + node game

Hey guys.

Im doing a first person shooter (multiplayer) using three.js and node serverside. Now the question, that i have, is, how do I do physics. First of all, player movement, so the player can not walk through obstacles and jump on crates and not fall into the ground. I gotta do this client-side (for prediction) and server side (so players can not cheat). I dont know, whats the best way to go here, since it also has to be done server side, it shouldnt be too expensive. Do i use a physics engine like cannon and just let the engine handle everything, client and server side aswell ? That seems quite expensive if I do that serverside. Do i rather implement shape vs shape collision functions by myself ?