Realistically, art on the internet doesn't get ripped off by anyone worth stressing over, unless it's top-notch—especially literature, art-thief types don't tend to go around thinking "I can make money off this poem". Hell, serious poets tend not to think that. dA is one of the better places online to post poetry without getting ripped off, because there is such a huge volume of it. More volume, less odds your piece is the one that gets ripped.
That said? deviantART isn't necessarily the place to get serious feedback on your work without putting a little effort in. It's a place to get community feedback, and a place to get solid feedback from solid writers, but the solid writers tend to be short on time and full of other people looking for feedback and critiques. There are some groups on here for Beta readers and critique exchange, but the better critique-exchange-type groups will require you to offer feedback to other members before submitting your own work. It is a good option insofar as it's a massive community where you can find someone to help you, though—just be leery of their qualifications.
I'd not bother submitting to competitions or journals without having gotten some feedback on my poetry overall, and not without getting some feedback on the first few pieces I was submitting from a published writer or an editor to get a "feel" for how to make my style print-worthy. Editors see a lot of poems, and (as harsh as this may sound) it's wasting their time to send them something that isn't up to the level of the publication. It's kind of like trying to release an album without anyone having ever said you were a good singer. Get some feedback, get some rewriting done, mull over the poems, read more, write more, then publish. Also don't delude yourself into thinking submitting to a journal or competition will get you feedback—it will, at best, get you a personal letter stating which poem the editor thought was strongest; at worst, you'll get a form letter stating "This really isn't right for us now, or probably ever, so good luck with your health, we're putting a gypsy curse on you."
When you feel you and your work are ready for publication, sites like Duotrope and New Pages maintain databases of magazines/contests/calls for submissions. It's hard to tell which magazines are prestigious if you're new to the scene, so I usually go through and see which ones print things similar to what I'm producing, or which ones reach markets I'd like to tap. The "This magazine has a funky name I'd like to put in my biography for future publications" strategy also works. For the most part, any magazine that doesn't charge a reading fee, doesn't accept reprints, accepts simultaneous submissions, and prints less than a quarter of the work submitted to them is probably legit; any competition that charges an entry fee is probably legit. Reputableness? Google them, I guess, and see how many people are bitching, and try to read old copies and see if they seem to have their editing-shit together in terms of putting a cohesive body of work in their issues/are printing actual quality poetry. Or get some friends who are published poets and ask them if they know anything, good or bad, about every mag you're thinking of.
Also, SUBMIT FUCKING EVERYWHERE. I have something like 50 submissions out right now. Don't submit to shitty places or places you don't have a shot in hell of being printed in (sci-fi mags if you write literary confessions, for example) but submit everywhere that you think could be a fit. You never know who might click with your work. Don't worry about it being rhyming, from an editing perspective I see so much shitty free-verse in the run of a day that a good sonnet would give me an erection and might result in marriage proposals.
As an aside: Don't ever expect to get paid for poetry. It happens once every fifteen years, on the full moon in August, when a hyena shits off the edge of a cliff onto a newborn baby holding a meat cleaver. Publish for the love of the art or for the love of your name in print.
Self-publishing poetry if you're not traditionally published is a crock of shit and a chafing masturbation session for your ego, nothing more. Let that comment make me unpopular; it's true. Especially with e-books, because you end up undervaluing your own work. Also self-publishing is all about your abilities to market yourself: Even if your e-book is free, no one will want to read it without you hooking your soul to them, unless they know your poetry well enough to know it's worth sitting down with. Also you have to think about things like layout design and graphics and all that other bullshit that we poets tend to be too flighty to think are important. Your words, when published, are only as good as the texture of the packaging they're stuffed into.
ALL THAT SAID: I'd suggest, yeah, for sure—post some poems on here. Join some groups. Get feedback. It's also a good way to learn to start marketing your poetry, making people on here read it. You might get some harshly legit feedback. You might get enough compliments to make you think you're ready to publish (you probably aren't, and should probably still solicit feedback). Make sure you're doing it as part of a well-balanced poetry diet: read poetry, write poetry, exercise poetry, workshop poetry, network poetry. This site's had some real success stories in terms of people coming here thinking poetry might be fun to take seriously and walking away from here published all across the world. You could be next.
All things considered, yeah, I don't expect to get ripped off, I just have paranoid friends whose fears tend to rub off I probably will start posting poetry on DA, maybe setting aside certain poems specifically for being posted online (ones I don't feel as insanely possessive over). Have any ideas on how to protect yourself if you do happen to have your work stolen? Short of a copyright lawsuit (not likely to happen ever...to paraphrase you, as likely as shitting full-moon hyenas), know of any steps to take to protect your work and prove you're the author, should a challenge ever come down the road?
Have any suggestions on the best way to workshop your poetry? I took a creative writing course back in college that was pretty much all poetry-related, having to create and recite our poetry for the class each week, but it didn't feel like a very critical environment (I think the professor didn't want to kill our self-confidence, and fellow students aren't exactly experts in the field). Are there any online poetry workshops you could recommend, or the best method to find constructive local workshops?
Another question that might be stupid and probably way down the road for me, but hey, I'm a beginner, gotta ask somewhere. I know a lot of journals/magazines/competitions require submitting poems that have not been published elsewhere. Is it acceptable to submit the same poem to multiple places that have that requirement (assuming it has never been published before), or should that never be done on the extremely rare and unlikely chance more than one place decides to publish?
I am that litigious douche who threatens lawsuits left and right, so it's hard for me to suggest what to do if you get your work stolen. Usually if I scream enough or impersonate a big enough legal team, people take stuff down. Granted, I've only had to deal with stolen photography, not sure if lit-thieves are as easy. I also scream at website owners and the likes. Anyone who'll listen.
I'm not much of a workshopper, personally. I have some poet friends and editor friends, and I just get them to review stuff for me. I have done a couple local workshops but wasn't impressed with the calibre of the people directing them. Not sure how to advise there.
When you look at magazines' submissions criteria, they will state whether simultaneous submissions are okay—if they are, then you can submit the same piece to any other mag that has okayed sim-subs. If one mag accepts it, you just withdraw it from the others. Duotrope can be searched by whether publications accept sim-subs, but they're not always 100% reliable in my experience.