Hi @michael_furey, welcome to the Vue forums!
To answer your main question, yes, Vue would be perfect for your front end. But then again, so would React, Angular, Svelte or any of the others. When it comes down to it, all the front-end frame works do the same thing and they are completely agnostic about how your website looks or acts. You can make whatever you want out of any of them. After all, the framework pretty much just controls the DOM/HTML. CSS is where you make a card game look like a card game.
However, everyone here (including me) would highly recommend Vue as the easiest to learn and most enjoyable to use
As for the backend, if you’re familiar with Lavavel then use that. I’m familiar with Meteor so I would recommend that as well, then you can write JS on the client AND server and get a database, reactive subscriptions and user-accounts system out-of-the-box. A lot of people here would recommend Nuxt.js since it’s designed to work with Vue.
Another option is to use firebase for your ‘backend’, then you don’t even need a server. Here’s an official Vue demo of using firebase: https://vuejs.org/v2/examples/firebase.html Vue is perfect for firebase because it can run completely in the browser without any help from the server. There are tons of Firebase/Vue tutorials on the internet.
My suggestion is to get your front-end card came working first. Then add a server/database afterwards if you want.
To get started with Vue you don’t even need to install anything, you can just start playing at jsfiddle, codesandbox or similar.