EDIT: Sorry, I was referring to Traditional Publishing when I said Vanity publishing. I was misinformed in the past and thought they were synonyms.
I apologize profusely for the misinformation.
I hate to break it to you honey but the first draft of your first book isn't going to be publishing quality. You're not even finished yet, so I doubt you've even read over the whole thing to make sure there aren't any typos. Please don't take it as an insult or get indignant, because I'm not dissing you as a writer at all.
I can speak from experience; when I wrote my first book at 13 and an entire community of writers told me it was amazing for a thirteen year old, I thought I was all ready to publish. But even five years later and after a couple of full manuscript edits I'm still not sure it's ready.
The longer you write, the better you get at it, and I can promise you that if you're still writing a year from now you'll look back at the first couple chapters of your book and literally laugh at yourself- not because it's necessarily bad, but because you can do so much better. The first draft of your first book is never, ever publishing read. Take a look at Twilight if you need proof. There's a kind of writing quality you can only get from experience- you'd be better off taking the time to make it better than launching into trying to get it published half ******.
HOWEVER, if you really want to try for publishing, you have two options; traditional or self. There are pros and cons to each.
Self publishing- you don't have to do anything to get published other than copy and paste your manuscript into a field, slap on a cover, and buy a copy. Wala, a printed book with no lines or hard work. The only problem with this is that you're a company of one- you have someone to print the book for you and that's it. You have to go talk to managers of bookstores all by yourself and get them to buy copies, and you have to hire your own editor, and you have to hire your own cover artist or use a crappy online photo editor with pictures you could get sued for using. It's a tremendous amount of work. Ebook self publishing is a slightly more lucrative means (50 Shades of Gray started as E-Book self publishing and hey, it's worth millions and a movie deal (Note: unless your book is twilight fan fiction porn it probably won't have the same response)), but you're still a marketing team of one. Getting your book out there is all up to you, and most self publishing books flop. You won't usually see them on the shelves of your local Barnes and Noble, certainly.
Traditional Publishing: AKA Getting a publishing company. This is a lot more work on the front end and a lot less on the tail end. You have to submit it to interns who read hundreds of (usually terrible) manuscripts from authors just like you a day, and hope they don't throw you on the slush pile. If they like you, they put you on the very small pass pile and send you on up the line. If their boss likes you out of the dozens of manuscripts they read, they'll be your "champion" of sorts and take you to the next round. Usually, only a couple of those next round books get published. The books published to books submitted ration is almost ridiculously small. Some people spend years submitting to every publishing company known to man pleading for a deal. It's not easy. But the company will get you a cover artist and an editor and if they're big name they'll get it slipped right onto book shelves for you. You don't have to market to the people, but you have to get the company to want you in the first place. It's a lot of formalities and frustration, but they're your best chance. I'd say 99% of books you hear about are traditionally published.
Also, to clarify, I didn't mean they're going to put up posters all over town. I meant that you don't have to personally talk to bookstore owners to get on shelves.
As for which publisher, it depends on your book. Different people want different things. You'll have to work around and find out who's good for you. But picking up a copy of writers market is definitely a good plan if you want to get published. They'll tell you who's looking and who's really picky and who even takes your genre.
Good luck!