Stomalomalus asked a similar question last month which might be of interest
Never had anything published, where to start?
Agents won't be interested in receiving short stories from an unpublished writer, not unless you've got enough to form a good anthology and you're famous in some way, so they don't come into the issue. (However, if you do get shorts published and/or you've been placed in contests, then to my mind it is worth mentioning in your covering letter if you're submitting a novel to agents even though novels and shorts are, as alex says, different disciplines.)
As for magazines and contests, write and submit to both -- contests will likely have theme restrictions and may cost you to enter, while it's free to submit to magazines but the competition may be fiercer. Just don't send the same story to a magazine and a contest at the same time.
Before submitting anywhere, though, do ensure the story is as good as you can make it. If you're not a member of a writing group or you don't have beta readers you can rely on, start getting them together now, they're invaluable. Meantime, use the Challenges and Critiques here to hone your craft, but do remember that if you put up work up here, it will likely be treated as already published (certainly if it's the whole story or the greater part of it) so won't be accepted elsewhere. (As a by-the-by, for instance, I won't accept a 1,000 word story for Kraxon which is based on a 300 Word Writing Challenge entry if it's basically the same story but padded -- it would have to take the original in a new direction in order to be accepted.)