No publication venue Should be beneath you. When submitting manuscripts, go ahead and send to big name magazines like The New Yorker and the Atlantic Monthly. But don't overlook small presses and magazines, school and business publications, community and special interest newsletters. Nor should it concern you initially if the only payment you receive for your writing effort is a copy of the document in which your work appears. What matters at first is building your portfolio, accumulating places where your work has appeared in print.
Volunteer editing jobs are great ways to gain experience.
I volunteered for two years as newsletter editor for the Nike AnimalRescue Foundation. I love animals, so this was easy enough to do. Where my own writing is concerned, I think of myself simultaneously as both an apprentice intern, and a professional. I take my work seriously, but I try to take myself with a grain of salt. Don't let any of the comments found here paralyze you into writer's block.