To install and use an Aarcade theme, all that is required is a Platinum or higher Big Cartel account - see Big Cartel plans and sign up.
You do not need to have your own web hosting to use Big Cartel or your Aarcade theme. Aarcade themes make use of your Big Cartel image upload tools for header, background and slideshow images. Our support articles also show you how to use a free file hosting tool for any custom page media content you require, e.g. images, videos, audio, PDF’s, etc.