The Elements of Style, by Strunk & White. This is one of those basic tools a writer needs to have on their desk. Did you use it in college? Probably. Doesn’t mean it is any less pertinent as you write your story. It’s cheap. Pick up a copy.
Writing Tools: 50 Essential Strategies for Every Writer, by Roy Peter Clark. While The Elements of Style gives you the basic rules, this book covers the tools you need to hone your writing, like activating your verbs and using dialogue as a form of action. It’s inspiring.
The Art of War for Writers, by James Scott Bell. This book is fun. The author cuts writing up in small, easily digested chunks and throws them at you to practice with. Lots of great exercises to get your writing skills in shape.
Nail Your Novel, by Roz Morris. Roz is a friend of mine and I can’t recommend her book highly enough. She walks you through creating your story, adding conflict, and making sure the story comes together the way it should.
Some extras you may want to consider:
These are books I’ve read that I feel are useful for fiction writers.
Make a Scene: Crafting a Powerful Story One Scene at a Time, by Jordan E. Rosenfeld.
Characters, Emotion & Viewpoint, by Nancy Kress.
Showing & Telling, by Laurie Alberts.
Plot Versus Character, by Jeff Gerke.
Story Engineering, by Larry Brooks.
Self-Editing for Fiction Writers, by Renni Browne and Dave King.
All of these books cover skills in storytelling that can only help a writer, especially one just starting out. Order them at your local bookstore or get them at Amazon, but make sure they are on your shelf within easy reach.