Why does Winston stop while reading chapter 1 of Goldstein's book in 1984?

As Winston is reading Goldstein's book, he realizes the importance of both the act and the work he is absorbing.  Winston recognizes the gravity of what he is reading and also understands that the act itself carries defiance.  It is at this moment that Winston has to pause in acknowledging the resistance he is exhibiting in both his act of reading and choice of what he is reading.  This is not lost on Winston in his pause while he reads:

Winston stopped reading, chiefly in order to appreciate the fact that he was reading, in comfort and safety. He was alone: no telescreen, no ear at the keyhole, no nervous impulse to glance over his shoulder or cover the page with his hand. The sweet summer air played against his cheek. 

Winston has to pause to appreciate the intense urgency of the moment.  He pauses in his reading because he is reading away from the prying eyes of Big Brother.  The work he is reading flies in the face of the Party and the Status Quo of control and repression that is intrinsic to Oceania.  It is for this reason that he pauses. In this pause, Winston recognizes that he is completely alone, immersed in a condition of freedom.  Seeing how this is so absent in Oceania, Winston pauses to appreciate it and to revel in it.  Orwell captures the metaphysical experience of reading, something that Winston has to absorb not only in the act of reading but in the sense of touch that accompanies it.  In touching the page and experiencing the moment, Winston pauses to immerse himself in an experience that many in Oceania are denied and an experience that those in the position of power wish to suppress from the body politic.

In 1984, why didn't Winston finish reading Goldstein's book?

Winston is unable to finish reading the book, in spite of his desire and interest to carry on reading Goldenstein's analysis of his world and society, because it is at this moment in the narrative that the Thought Police decide to reveal there presence, which has been there all along, and arrest them. They realise that there was a telescreen hidden behind a picture all along, and that their secret hideaway was never secret and was carefully created by the Thought Police precisely to ensnare them and record evidence against them, which will no doubt be used as they are taken to the Ministry of Love. Note how they realise finally that the game is up:

"We are the dead," he said.
"We are the dead," echoed Julia dutifully.
"You are the dead," said an iron voice behind them.

It is the sudden and ironic repetition of this phrase that indicates the presence of somebody else. Note how the phrase foreshadows the "death" that Julia and Winston face, making it an appropriate phrase to be repeated by the Thought Police.