They’re undeniably useful. A picture tells a thousand words, and all too often the picture tells you everything the reader wants to know and sometimes more: it depends on the quality of the picture. Given how well some artists do, it will almost always portray what you want it to. Sometimes you only need one: sometimes you need a plethora.
However, here’s the beef: do you really need illustrations to make your book good? Look at the reason for why you want an illustrator to do some work for you. Is it just a neat little touch, something to get more sales, an obligation, or something to adorn the cover with?
I hope you answer is not “because I think it will help me tell the story”. Nuh-uh. Wrong move. If your story has a weakness if it’s not illustrated, it’s back to the drawing board. Begin the editing process again. If you need to give your readers visual aids, your book must be pretty sorry indeed. Don’t fall into this trap: learn to use mental pictures to write your story independent of illustrations. Trust me, it’s better that way.
However: I’m not decrying illustrations: far from it. I just wanted to get over that initial hump: if you need an illustration to help tell the story, it’s the story that needs revision. However, there are multiple good reasons for wanting art. The most common of these is the craving for cover art.
I’d say this is your cheapest and best option if you’re going for art. You only need one image, which minimizes the cost. If you can find a good artist, you instill one good image in the reader’s mind, and (if they like it) it inspires them (hopefully) to read the whole book.
A good cover illustration serves as a first impression. First impressions are everything, right? I like to joke with my dad about the fact that we say “don’t judge a book by its cover” when, in reality, we can take one look at a book or movie with a poorly-made cover and not give it a second chance. Even though we quote the old idiom, the world of book cover designers know that we believe exactly the opposite. Chances are, if you don’t like the cover, you won’t read the book. End of story.
A well-placed illustration can help with this: it can instill a lasting idea in your readers’ minds, causing them to view your book in a new light. It gives them a lens by which to read the book. Like your writing, it gives them a frame of mind in which to think.
Then, there is the kind of person who wants an illustration every other page. Even if you can afford this (which I highly doubt you can) I would not. A multitude of illustrations can draw the reader in further, but only shows how low-quality your un-illustrated work is. Your work should speak for itself, almost literally.
The multitude of illustrations can often bog down storytelling, as well. The pictures don’t tell the exact story that the story itself does, so there’s bound to be at least some confusion. I would just pick one fun illustration and use it for the cover image, regardless of how many you get.
But don’t ask about children’s books. They’re for children, so use illustrations. Lots of ’em.
Good luck, and happy writing!