Most writers aim to be published, and this is no bad thing. But it is better to aim to write well and to treat 'publication' as a separate activity. Over the years, I have discovered that it is useful to always review the broad range of outlets for publishing, since this allows would-be professional writers to understand the kind of work that is potentially read. Moreover, it is also useful to have something to aim for. In other words, to be published is a great boost to one's writing career, but it is better to merely use the possibility of being published – or the possibility of winning a writing competition, to complete one's current writing project.
(The sub-links from the 'Publications' menu provide a list of published work to date).