I only have experience with traditional publishing, so I can only advise on how I'd proceed on that route.
With traditional publishing, you will likely find it very hard to get a short story published unless you go looking for magazines or websites that accept short story submissions. Getting a short story published in an anthology often comes down to who you know and what books you already have published. It's highly unlikely that a publisher is going to publish a short story on its own, due to the costs involved and lack of expected return on investment.
So if you want to go with finding an agent or a publisher, I would recommend going with the novel.
Now, that said, what you could do, as Dresdenus suggested, is self-publish the short story first, then if it does well, refer to it in your query letters to agents and publishers. But, whether you go with self-publishing or traditional, if you do decide to self-publish the short story first, I would strongly recommend you hire a professional editor and cover designer. It'll cost you, but think of it as an investment; the more professional your work looks, even if you release it for free, the more likely others in the industry will want to work with you in the future.
