There are timeless books that people like to buy and use over and over. There are other books that are useful at a given period in a person's life or for a specific task and then end up in a garage sale.There are books you can find in the public library, and other books you can't.
If you don't already have one, consider creating a lending library at your church for books that kids (or adults) won't find in their public library, especially books that are age specific and discarded when a child outgrows them. (Bible story board books and very short easy reader Bible stories.) If you buy them new you're feeding the author and illustrator who created them. That's a good thing. If you recycle them (collect books from families who no longer want them) it's good stewardship and the project becomes very affordable and benefits many. Also a good thing.
Examples: Books with Bible stories or Christian themes or world view. Especially books that are destined to go out of print or books that kids won't find in their school or public library. Board books, picture books, pop-up books, seasonal books, emerging or early readers - particularly the very short, very easy Bible story books that parents don't buy because kids may read them 3-4 times and they move on to harder books. Arch books are nice by they are too hard for beginning readers. Fiction for all ages. Bible, church history and traditions, Christian heroes. History through the eyes of praying people who were there. Leveled readers that might be used in a Christian school. Books that people (particularly children) won't find in public school or public libraries that will reinforce or kindle a love for learning and for scripture and for God. Faith-inspiring books. Hi-Low books and graphic novels (comic book format) for older reluctant readers (particularly boys).Stay away from the boring, colorless books for boys and your youngest readers. Colorless, pictureless read aloud books.
Think voracious readers but also think reluctant readers, especially boys. Building a library like this might be a fun project for pre-teens, teens, parents, or young adults. I'd say grandparents but as far as choosing books that entice today's kids to read, make it a project for younger groups. As far as timeless books, much loved by many generations, age won't matter. Retired adults or empty nesters might enjoy buying books or donating money to buy books or replace well-loved, worn out books.
The goal: to collect books that people might not buy or can't find in a library that might serve a particular age group, particularly emerging readers - tools to grow a child's reading skills and faith.