So I wrote a short story it's about 15,436 words it's going through a proofreading right now so all of the grammar spelling/ wording should be fixed but what do I need to know about publishing should I go through a publisher or should I self publish my work?

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I think you should look towards magazines that specialize in short stories or perhaps try to publish it on a website, like vocal or media. You can always try self publishing, but that isn't always easy and will probably lack creditably.
You could always try going through kick starter or a different site like that.
Yah a magazine isn't going to work. This it's just a test run story before trying to publish the 75,675 word book if I'm going to fuck it up I'd rather it be on something miner
You could try publishing through a major publisher, like Penguin House, but I am fairly confident that would be much harder and they probably won't do it.
I would say publish the short story in a magazine or on a website and then when that is published go to a large publisher with your book. If you can publish the short story first, through a business then you have more credibility for your novel, which will dramatically increase your chance of being published.
A publishing company won;t even talk to you without an agent. Your best bet is self-publishing, but you're going to have to get creative as far as marketing, since thousands of books and novellas get published every day on Kindle.