When you’re an aspiring writer, any offer to publish your writing should be accepted graciously!
Now, I don’t necessarily mean vanity presses, but that’s a post for another day. Any competitive press or literary magazine that would like to publish the manuscript of your novel, poetry, or short fiction should (in most cases) be accepted wholeheartedly.
There are certain places that everyone would like to publish with. Of course you’d probably like to publish with The New Yorker, Granta, Glimmer Train, Tin House, PANK, Word Riot, or any of the Big 5 publishers—so would every other writer; that doesn’t mean that the obscure journal with a subscription list of 1,000 should be overlooked.
The fact is that any competitive press is just that—competitive. They screen out lots of writers’ work. If any publisher or press likes what you’ve sent them, that’s a huge victory. It’s not a slight to get published somewhere that isn’t widely known, even amongst literary crowds. Keep in mind that the big publishers pay attention and are always scouting for new talent. If nothing else, you are building quite a portfolio.
The reality is that it’s just not common for most writers to start at the top of the heap, unless they have a wide platform from being notable for some feat other than writing. If you have the chops to get published, no matter where, that’s a huge victory. Embrace it. The journals and presses that you may be seeking to publish with quite possibly may take note, and soon you will be on your way!