My two cents is...why? Promotion is something that happens when you have a product that you want to encourage people to buy. You don't have that yet. If you have to do something, register a domain name in your author name and put up a very simple website that maybe includes a short bio, your social media links, and a brief description of the story you'll be seeking an agent or publisher for. That's not promoting your story--it's promoting yourself as a professional.

If you decide not to pursue trade publishing and self-publish your story, then the answer maybe the best first step is to decide exactly what it is you want to do.