You can do both. My husband started watching the series and on another forum we are both on, a lot of the people there had already read the books and said the first season was a pretty faithful adaption. We bought the books and my husband's finished all of them. I just barely started book 3.
I've heard rumors the next season may be a mash up of books 2 and 3 which would be a good thing. Book 2 has a lot of just walking around with most of the characters so I felt I had to be patient with it. I did enjoy the ending though. I hope book 3 picks up the pace a bit more. I don't need endless amounts of action (especially in books) but a fair amount of action in between quieter parts are good especially in an epic such as this.
I've heard rumors the next season may be a mash up of books 2 and 3 which would be a good thing. Book 2 has a lot of just walking around with most of the characters so I felt I had to be patient with it. I did enjoy the ending though. I hope book 3 picks up the pace a bit more. I don't need endless amounts of action (especially in books) but a fair amount of action in between quieter parts are good especially in an epic such as this.