There is a great division of opinion on this issue and some of my peers would disagree, but I generally recommend approaching publishers first, simply because I've known too many writers who have lost years waiting around to hear from agents. Some publishers, however, indicate that they will not accept unagented submissions. If your query letter is exciting enough, maybe they'll make an exception. Some publishers indicate they won't accept simultaneous submissions. Indicate in your cover letter that you're making simultaneous submissions and then generate as much action as you can.
Many publishing houses have tip sheets.
Write for them. Writer's Market is also an invaluable source for answers to all these questions. I hope these suggestions help you on your journey to becoming a published author. Remember, however, that writing may be what you do, but it's not who you are. You don't have to be published to take joy in the process of writing.