Introduction

Vue is good choice because of two reasons in your case:

1. It is simplest to learn than Angular and React

2. It is progressive - it means you can easy use it only in constrained part of your existing project.

If you look at dock of life cycle of Vue instance

https://v2.vuejs.org/v2/guide/instance.html

You will see there are some options of create template and connect it with instance of vue.

a) by "el" option - selecting existing element from dom

b) by template option

• including template as a string

• selecting template by id of script with type text/x-template

You can use Vue instantly after page load or mount it later so you have flexibility.

Examples

I understood your question is about simplest way to integrate vue with drupal. I think that these examples of use Vue on simple html page will help you.

Simplest way

Simplest way is use el option and load Vue from cdn. ( remember about change cdn to minified on production )

<style>
    [v-cloak] {
        display: none;
    }
</style>

<div id="app" v-cloak>
    <h1>{{ heading }}</h1>
</div>

<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.13/vue.js"></script>

<script>
    new Vue({
        el: "#app",
        data: { heading: "Hello World" }
    });
</script>

By using text/x-template

<div id="app"></div>

<script id="app-template" type="text/x-template">
    <div>
        <h1>{{heading}}</h1>
    </div>
</script>

<script src="https://cdnjs.cloudflare.com/ajax/libs/vue/2.5.13/vue.js"></script>

<script>
    let v = new Vue({
        template: `#app-template`,
        data: { heading: "Hello World" }
    });

    v.$mount();

    document.querySelector("#app").appendChild(v.$el);
</script>