It's the harsh reality of being a writer that unless you're a celebrity (not even in your own field but the Hollywood-type), it's really difficult to get anything published. And that includes getting the attention of literary magazines and online journals, too.
In today's publishing world, sometimes it's important to go where new writers are actually wanted. When applying to literary agents, you'll often find that they don't want to talk to you, unless you've already been published by someone else or unless they talk to you first. This is what they mean by "No unsolicited submissions". (And yes, they really mean no. Just cause it's good doesn't mean they care.) And even when you do submit to the ones who accept submissions, it's often a six month process before you even get a polite rejection notice in the mail.
So, for now, if you're at the beginning of your writing career, go to places where they actually want you. Last week, I suggested a writing a romance short story, and here's why: romance sells bigger and better than any other genre.
One of the world's largest and most profitable independent publishers is Harlequin. Harlequin is of course known for its series of grocery story romances - from their sweetly told cowboy stories to the erotic danger of their Harlequin Blaze line (Raunchy!). Harlequin broke the genre mold by generating lines of books that were similar in style and tone, so that readers knew exactly what type of book they were getting under each banner.
And of all the publishers, I still think Harlequin made the best transition ever into e-publishing. They took their old branding and recommitted it online, allowing that each series now produces new stories monthly or even weekly in ebook form! (I heard a rumor that one line is nearly daily and that's just insane, since they wouldn't be doing it if it wasn't profitable. But I don't watch Harlequin's publishing schedule close enough to know if there's truth to this rumor.)
So what is the point of all this? In essence, go where the money is, because a publisher who publishes that much material needs to be constantly buying. Also, Harlequin will take submissions directly from their authors - there's no need for an agent. As far as commercial fiction goes, they're probably the largest publisher to do this. This will save you lots of time and money.
If you're as good of a writer as you think are, you should be able to write a wonderful romance story. They're formulaic, and Harlequin's submission guides will tell you exactly what you need to know. Read several of their books first to get a feel and then give it a go. You might even enjoy it.
You could be a published author, published by one of the most respected publishers in the biz, by next fall (or even earlier) if you do it right. And you have a far better shot of this than ever getting published in Atlantic Magazine or even The Kenyon Review.