Production and Staging environment question for experienced devs

I've got something going that uses wordpress to handle a lot of the backend stuff and want to move it to a server, create a staging and production environment and start a standardized release cycle.

I'm considering using wpengine as I like their bundling of security, caching and scalablity as well as how focused they are on keeping everything wp-related tight. However, they said they don't allow SSH (they do have a git tool) which means I couldn't use package managers or build tools like gulp or grunt on the staging server.

My questions is this; is that even important to have those tools on a staging server? Do teams even use that sort of thing or are they only used locally to develop and staging is just that; a place to put your code to view it in a live environment before moving it to production?

I guess that part of the process is bit fuzzy since I've learned in the past year on my own and am basically cowboy coding right now. However, I want to make sure I get this right since I'm wanting to bring on a small crew at some point soon.

Any advice on this or even a way to get the security and caching options of wpengine but more access (if I even need it) is appreciated.