I know it seems like publishing = good, and not publishing = bad, so in order to be good you need to get published...
Here's the thing: publishing and writing are two wildly different monsters. You can teach yourself to write (or study somewhere to get better) without publishing at all. Or you can publish something, and in the interest of getting published more, keep writing the same thing--and you might have a lot of credits, but artistically you've done nothing.
Writing is the long, lonely hours. Writing is locked behind a door, neglecting friends and family, and being regimented in your approach to getting better. Writing is reading a lot of different things. Writing is indulging every thread of an idea, and riding it out to see if there's something in it. Writing is a sore back and getting fat because you're always at a desk. Writing is the smile at 2am when you finish an edit and think, "oh man, I think this is really good." And writing is looking at the same piece in the cold light of a blue morning and saying "No, it's shit" (if it is). Then doing it all over again.
Publishing is sending emails, studying and supporting magazines and small presses. It's sending out your shit with stamps, and envelopes, and submitting via mishmash. It's tracking your submissions, and following guidelines, and establishing relationships with editors. It's being professional every time you get a reject. And it's doing it every goddamned day, for years on end, with nothing to show for it but contributor's copies.
They have very little to do with each other. I know you might think that publishing something will legitimize your work for you somehow--and it's true, it might. In that case--it's probably worth it. A writer needs to absolutely believe in their work. But if you publish just to say you're published--then deep down you'll always know you aren't--not really, not like you wanted to be--and that will actually work against you, and you won't get the confidence that you thought being published would give you.
My advice is to be patient. Separate the 2 in your mind and keep working, reading, and trying to figure out what your favorite writers are/were doing. Keep studying and submitting only to the mags where you think your work fits best (and be honest, if you can't get into Scratchy's Xeroxed Zine Crotch then don't submit to the New York Quarterly--you're wasting stamps). And once you garner a few publishing credits, think about putting together a chapbook manuscript. By then, someone might ask you for a manuscript, and all the worrying about it will be moot. Best of luck to you.