One good story for first graders to read is "Don't Let the Pigeon Drive the Bus" by Mo Willems. Another story that is suitable for a first grader is "The Grouchy Ladybug," according to GoodReads.com.
"Don't Let the Pigeon Drive the Bus" is about a pigeon who really wants to drive the bus after the driver asks for someone else to take over during his break. The pigeon throws a temper tantrum, trying to get his way.
The story of "The Grouchy Ladybug" by Eric Carle describe a ladybug who is not afraid to pick on animals larger than her. Children who read this learn about the consequences of bullying.
"Splat the Cat" by Rob Scotton is another winner among first-grade readers. Splat, who is nervous about his first day of school, brings along his pet mouse. Just when Splat starts making friends and learning new cat things, his mouse escapes, and all the other cats start chasing Seymour the mouse. The teacher wrangles the class back together, and they all learn an important lesson.
Shel Silverstein's "The Giving Tree" teaches the importance of friendship and not taking advantage of those friends. A boy learns that the tree gives him everything it has, and he has to learn to take care of it in return.