Alan Rickman was handpicked to play Snape by J.K. Rowling, and received special instructions from her about the character. Rowling even provided him with vital details of Snape's backstory, not revealed until the final novel.
Richard Harris had trouble remembering his lines, and Daniel Radcliffe would ask him to help with running his lines, just to give Harris more practice.
Casting Harry Potter was the biggest challenge; they saw 5,000 boys audition, and none of them felt right. Producer and director Chris Columbus saw Daniel Radcliffe in David Copperfield (1999), and showed it to the casting director, and said Radcliffe was the one, and that he was amazing. But she said they wouldn't get him, because his parents want him to focus on his schoolwork, and not acting, as well as all the attention he'd get. So they interviewed Harry Potters of different nationalities all over the world, and still hadn't found him. She got frustrated with Columbus, because he had his heart set on Radcliffe. By sheer coincidence, the producer and screenwriter of this movie went to a theater, and in the front row was Radcliffe with his father, so they talked, and slowly persuaded him to cast Radcliffe.
The child actors and actresses would do their actual schoolwork in the movie, to make the school setting more real.
Richard Harris, who had been acting for more than forty years by the time this movie entered production, stated that he had never been involved with a cast that was as close as this one.