Building your classroom library takes time. It will change as your career does over time and with patience.
Helpful suggestions to get your library up and running:
-look at thrift shops such as Value Villiage, or Talize for books, there are always gems there
-garage sales in the Spring and Summer
-local book sales at churches
-create an account with https://www.scholastic.ca/ they will sent you flyers to hand out to students in your classroom. Also, teachers receive a bonus when students order and that can be used to give back to the classroom
-librarians sometimes purge books from the school library, I always look for books at this time, especially for non-fiction books that can be used for your content subjects
Organization of Library
This really is personal preference. In the past I have had indiviual bins that are sorted either by author or genre. For example, Robert Munsch and Mo Willems would have separate bins. There would also be generic 'fiction' and 'non-fiction' sections for students to look at.
In my current Grade 1 classroom I have one small book shelf. I put new books out every month to rotate what is there. It is based by theme (time of year, holidays), but there are always generic fiction and non-fiction books, as well as books with diverse characters. I have been adding books to my diverse library each year to incorporate books that represent the students in my classroom. I store the books when not in use in plastic bins which are hidden in a nook in the classroom. I also use an app called BookBuddy to organize my books. I have entered every book from my collection and put them in bins according to where they are in the room. I have also separated my books into cupboards that I use for different subjects. These are picture books for Math, Language, Social Studies, Science and Art. Students of all ages can benefit from picture books even when you are not specifically teaching a Language expectation.
I also have a separate section in the classroom where my decodable books are sorted by phonetic code. There are alphabetic principle, CVC, Blends, Digraphs, Long Vowels, Marker 'e' (also known as silent/bossy/pushy e), and R controlled vowels. These books are available to students as we learn the strategy and we practice by ourselves, or with a partner during repeated reading sessions in the classroom.