I'm answering this in depth only because I love vue and want you to eventually succeed at it.

if you are not a total beginner and know javascript very well, start with riot instead of vue. riot has fewer conceptual abstractions so it's easier to wrap your head around and doesn't require a complex build system. as a vue user, it will already make sense to you -- using single file components.

if you are truly a beginner:

don't start with javascript at all. start with HTML and CSS. this is how you'll learn about progressive enhancement as you begin to introduce javascript. (in production, you may need to satisfy tor browser i.e. noscript users, non-Google bots for SEO, richard stallman, etc -- so your site must function without javascript, or you're ruining the web. this is just my opinion).

good CSS, if you work on a team, is critical, and almost no one gets it right. use sass, a grid mixin library like susy, and autoprefixer to start. because your username is "pythonicpro," I am assuing you're a python user, and would recommend you apply to your sass the same sort of sanity that python applies to indentation levels. sass allows you to endlessly nest things. this is bad, and a common mistake. also, because python is a whitespace-y language, you might look at pug (formerly jade) for making your HTML simpler.

don't use something like bootstrap, or if you do, only use it for a day to understand the grid and then move to susy. grids are important. learn about grids in a book called "grid systems" by josef muller-brockmann. you will be disappointed by that book. learn to be disappointed by that book because it is a very good book and one day you will not be disappointed by that book. do not use flexbox for layouts or things will look weird as they render on slow connections.

once you get to javascript, you should probably stop using all javascript frameworks including jquery if you're just getting started. yes this means you'll have to type "getElementByID" and "requestAnimationFrame." there are worse things in life (like trying to use frameworks or complicated build tools when you don't know how and why they work). consider using ES6 (my recommendation) or typescript (many others' recommendation) for the javascript, because this is what the frameworks you'll eventually want to learn use. both es6 and typescript work with vue and react, but angular is typescript-only. consider strongly using gulp for babel, typescript, es6, autoprexfixer, sass, etc.

once you are comfortable enough with this stuff, start working on your design abilities. if you have any autonomy at all in your job, you have no idea how much easier it will be for your designers if you speak design. (this is why grid systems are so important). learn about typography, because that's most of what web design is. be smart about CSS em and rem units. be smart about the size of your font files: ask your designers, "have you removed all of the glyphs from the font file that aren't in languages we support?" look up why an em is called an em. learn about colors that are compliant with disability standards. learn about whitespace. read kenya hara's "white." be disappointed by kenya hara's "white." learn to be disappointed by kenya hara's "white." you're well on your way to pleasing your designers.