Top-down, or realistic?
As an amateur/unpublished writer, do you really want to "waste" the New Yorker's time? Is there really the chance that you're the breakout undiscovered super-scribe? On the other hand, does it do you any good to have a realistic goal with your writing considering the amount of pavement-pounding one must do to achieve even an MODEST placement in a litmag?
I say GO FOR IT. True, a literary magazine may shovel your work back into the envelope with haste and fury, slapping that SASE back into the mailbox faster than you can say "wait!" but they know your name, now, even though it is as an object of burning scorn, a red, swollen blotch on a day that was otherwise pleasant. And that's fine, just... next time send them something better. After that, something even better. Then a better piece after that. Etc. They'll see you growing. Perhaps that will encourage them to publish your work? It could happen, I mean, at least, I think it could. I imagine it could. Right?
I mean, I don't know, don't look at me for advice, though... everyone thinks my stuff is too WACKY to appear in their magazine. They've got a public to think about, people. They can't have my ramblings sandwiched, shoe-horned, if you will, between advertisements for the Iowa Writer's Workshop and a fancy watch company like "Omega" makers of the acclaimed Seamaster series. How would that look, a story about owning a pet shrimp, slapped in between those two advertisements, those fine purveyors of their craft and trade? How it would look is, people would think the "The Iowa Writers Workshop is obviously a beastly hippie commune that espouses hard substance consumption as a means of simulating creativity, and the Omega Seamaster watch is clearly not the sort of product I should be getting involved with. It will probably cease to work right when I need it, or magnetize my credit cards or shoot springs and gears at my grandmother in a malicious fashion when I'm not looking, and then phone to have her placed in a dodgy old-folks home. Also, as I read this magazine I feel that the ink may be lead-based."
On the other hand, your writing may not improve and you may not have the option to send a increasingly better work of fiction each time your submit. If that is the case, no problem, there are still options (and most of them are not even suicide!).
Consider, instead, becoming the editor of your OWN magazine!
You could also become a blogger. OH SNAP, THE JOKE BECOMES A MIRROR TO WHICH I HOLD MY OWN EXPERIENCE UP AND SAY "GEE GOLLY, WOULDJA LOOKIT THAT."
