If a publisher is legit, the publisher picks you. Not the other way around. You query a publisher (or your agent contacts the publisher), and the publisher decides if your book fits their needs. Mainly, can they make a profit by selling your book to readers?
In one of the online groups I belong to, not long ago an aspiring author asked the other members if we knew a "good publisher" for her novel. "I've finished mine and want to find a good one that isn't a self-publishing place," she said.
Hmmm. I'm not sure what she means by "finished." Completed the first draft? Workshopped it through a writers group and revised it? Gotten input from Beta readers and revised again? I don't know. But I do know that many aspiring authors think a manuscript is finished as soon as they type the words "the end." It usually isn't.
Nevertheless, her question got me thinking about how to tell legit (commercial) publishers from the other kinds (vanity, subsidy, self, etc.).
One way to tell: Check the publisher's website. What is the business of commercial publishers? To sell books, of course. To whom do they sell these books? Readers, of course. Therefore, the website should show that the publisher is in the business of selling books—not touting what it does for authors, not bragging that it has revolutionized publishing, not openly soliciting authors, not comparing itself favorably to other types of publishers, not professing to support a particular religion or a particular cause. Granted, the publisher should have a link to its submission guidelines somewhere on the site, but the homepage should be about the books this publisher has published.
Check out the websites of the big-name publishers. The homepage for Random House (a division of Bertlesman) features some of their latest books as well as a list of their best-sellers, news about their featured authors and their recently-published books, and other information for readers. Clicking a book cover leads to ordering information from either Random house or a host of retailers—and to more info about the book. The website makes it easy for readers to learn about books. Way down at the bottom is a link to click for submission guidelines. Clicking it lets you know that they don't take unsolicited submissions.
Meanwhile, read this Glass Cases blog post that contains good advice about both agents and publishers: "Shady Business." Maybe read it twice.