I've talked to a lot of writers, including published writers, some of them famous, some of them not. Most of them agree that when trying to get work published, don't dismiss small presses, little literary magazines, or other lower circulation venues. Get your work out there, become part of a writing community, become read, and don't be a snob.
It's worth noting that John Grisham's first novel, A TIME TO KILL, was rejected by every major NY publisher. So Grisham self-published. While he continued to improve his writing craft, he and a group of friends sold copies of the book out of the back of his station wagon at flea markets and county fairs around the South. Eventually, THE FIRM was traditionally published and people started asking, "What else have you written?"