I am currently using PaperJS in a few projects, for which I'm using the regular download links on the website: http://paperjs.org/download/.
I see PaperJS can also be installed through NPM, although it requires a bunch of dependencies as explained on this page: https://www.npmjs.com/package/paper#installing-paper-js-for-node-js-through-npm
My project does use NodeJS on the backend, so is it better to install Paper through NPM? If you can just use Paperjs by downloading it from the downloads page, why would you need (or want) to install the Cairo Graphics Library and the rest?
Installing paperjs with npm is how you would install it to be used in nodejs as opposed to in the browser. If you want to use it in nodejs then there is no DOM or browser to support a canvas and the associated API. That's the reason you need to install cairo.
If you're using paperjs in the browser then it doesn't matter whether you're running nodejs or apache or bottle.py as the backend. Just download the library and use it as you have been.
The whole purpose of running paperjs in node is to be able to run applications entirely within nodejs with no browser present.