The characters in this story are all very interesting, especially that of little Paul and his money-loving mother. His mother is described in detail in the first paragraphs of the story as a rather vain, materialistic woman who feels slighted that she does not have more money in life. Also, an interesting fact is that she does not love her children; in fact, it says that "she could not love them" and that when they were around she felt "the centre of her heart go hard." She tries to work here and there, and whenever she does get more money, she uses it foolishly instead of wisely. Despite her lack of love for her children, she pretends to love them, and at the end of the story, shows a lot of concern for Paul before he dies.
Paul is the main character; he is young, intense, and focused on gaining his mother's love through the use of "luck," or money. He is single-minded in this task for over a year. He is sincere, intensely dedicated, trusting as he enters into partnerships with his uncle and gardener, and a rather haunted, disturbed little boy.
His sisters, father and governess are not dynamic characters; rather, they are just in the background and make a brief appearance every once in a while. They don't impact the storyline as much as Paul and his mother. The only other two characters that make a difference are the gardener, Bassett, and Paul's uncle, Oscar. Bassett is a kind, trustworthy person who did the best that he could with Paul's proclivity for guessing winning horses. He never cheated Paul on the races, and was very kind and fair. Oscar is a bit of an opportunist, jumping in on the Paul bandwagon when it becomes apparent that Paul is always right, but he still treats Paul fairly, helping him to manage his money.
I hope that those descriptions help to get you started; good luck!