What is the best way to deploy a Craft CMS 3 site?
At the risk of offering a "link answer", the Setting up a New Craft CMS 3 Project has a section on DEPLOYING CRAFT CMS that should be useful to you.

I've never heard of Rocketeer, but popular ways to handle deployments are via buddy.works, Laravel Forge and the like. We talk a lot about this on the Website Deployment without Tears episode of devMode.fm