This is the third entrance related to Visual Studio Code. In the first one, you can read how good it is, in the secontd, you can red some of my recommendations and get the best performance including some good extensions, and in this one, what you need if you want to work with VueJS.
Javascript Vue
Because I don’t use helpers but Javascript files for developing with VueJS, this extension can help you a lot, because it supports Vue in .js files.

Vuetify
Vuetify is the framework I like when developing with VueJS, and of course, there is an extension to help you.

Snippets for Javascript
Code snippets are templates that make it easier to enter repeating code patterns. There is several extensions, including JAvascript. In general, the best snippets that you can have are your own, and this feature will increase your productivity (at least, this is my case).
In addition to the snippets, I recommend you try ALT+up or down for full lines up or down. Refactoring is also another strong point for editing code.
Vetur
Vetur is another basic extension for working with VueJS.

Vetur includes a lot of help to work with VueJS: Intellisense, snipets, syntax, formatting, … It is convenient to know everything that is included, because it makes things much easier, although some functions require other additional extensions, such as ESLint plugin, VS Code Snippet Syntax, …
Vue 2 Snippets
Perhaps, it is less complete than the previous one because this extension is dedicated almost exclusively to having code shortcuts:

Vue-beautify
If you need an extension to keep your code in perfect condition, this is your plugin:

Un resumen de extensiones para trabajar con VueJS
As you can see, there is several good options for developing with VueJS, Vuetify, and all you need, but the normal way is to try some extensions, and those who adopt best to your way of programming, keep them, and unistall all extensions that you don’t need or don’t like, in order to overload Visual Studio Code.
Other interesting extensions are Firefox for debugging, or Chrome for debugging, …. Too much to choose from!
Happy coding!