SOLVED: Best way to deploy Craft 3 to webserver?
At the risk of "link" answers, we talk about different deployment strategies here:


Website Deployment without Tears


...and there's a writeup of deploying Craft CMS here:


Setting up a New Craft CMS 3 Project


It's hard to do a TL;DR on this, because it's fairly involved, but essentially ignore your vendor/ directory, and do a composer install on your production/staging server to install the vendor/ directory there, synced up with your composer.lock

Using some kind of deployment tool like Forge or Buddy.works will also make your life easier.