I would suggest Cookies! If you add the items to cookies, you can set them to auto-expire. For example, if the user has added something to the cart, you can automatically delete it after 2 months or so. Another advantage of Cookies is that you can set it from Server too. So in order confirmation page or something, from the server itself, you can delete a user's cookies
But if you don't want to expire it, then go for LocalStorage. LocalStorage is more easy to set, get, delete etc. Since you're not using any front-end libraries you'll need to create functions for handling cookies (only a few lines though)