Edit in JSFiddle

<button data-id="1.css">1</button>
<button data-id="2.css">2</button>
<button data-id="3.css">3</button>
<div id="current"></div>
.active {
  background: yellow;
}
init()
document.body.addEventListener('click', onClick)

function init() {
  const curr = localStorage.getItem('currentCSS')
  if (!curr) {
    localStorage.setItem('currentCSS', '1.css')
  }
  render()
}

function render() {
  const curr = localStorage.getItem('currentCSS')
  document.querySelectorAll('button').forEach(b => b.classList.remove('active'))
  document.querySelector('button[data-id="' + curr + '"]').classList.add('active')
  current.textContent = curr
}

function onClick(e) {
  if (!e.target.matches('button')) return
  localStorage.setItem('currentCSS', e.target.dataset.id)
  render()
}