This play was acted on stage in New York City, but you are too young to be familiar with any of the actors and actresses that played Mary and James Tyrone, Edmund and Jamie so you will have to come up with modern actors/actresses that you think fit the parts.
The analysis here on eNotes might help you. Mary is a drug addict -- so, which modern actress do you think could play this part? It is a difficult role that depicts a complicated woman who has suffered greatly in life, and the actress must be capable of portraying challenging emotions. So, I would pick an actress that has won some academy awards -- like Meryl Streep. She is so versatile, she could probably play any role. James Tyrone also requires a strong actor. He is a difficult man to live with, on the miserly side, and his sons blame him for their mother's addiction. In fact, all of the men are rather dismal characters, Edmund has just learned he has TB, his brother Jamie is a drunk, the father drinks too much, and they all get drunk as the play progresses.
Who do you think would make a good James Tyrone? Jack Nicholson? Hal Holbrook? Maybe Dustin Hoffman? They have all won awards, so they could do it. It would have to be an older actor. What about the sons? Tom Hanks? How about Russell Crowe?
There is a good summary of the play here on eNotes to help you with your summary.