Questions about Rolands quest in the first book and then others (spoilers)

I'm looking for help remembering things about the book series.
From what I remember in The Gunslinger Roland originally is chasing the Man in Black to get revenge for what he did to Rolands mother. Correct? The Dark Tower is mentioned but it isn't until the end of the first book we learn his real purpose is to climb the tower. During Wizard and Glass Roland sees in the Grapefruit that the Tower is in fact real and that's where his journey starts for the tower? Is that right or did I get things wrong?

I think that's more or less right.

That's one of the problems with writing prequel stories. It tends to muddy up the waters of the stories that came before it.

I didn't start reading the book until the series was done. I ended up reading the version of The Gunslinger that was an extended version. I remember that Roland catches Marten or whatever his name is with his mother and then out of rage challenges Cort to his test for his guns. Like you said Wizard and Glass is mostly a prequel that goes into more depth why Roland is doing what he's doing. But in the first book Stephen King makes it sound like his original purpose is to chase after the man in black and kill him for what he did