I highly recommend Saiyuki Gaiden. Story wise the Gaiden arc is amazing and definitely my favorite Saiyuki story. It's by far my favorite prequel and one of the best i've seen. It has a brilliantly touching plot that leaves me crying every time, and the character relationships are heart breaking and beautifully depicted. The Gaiden left a strong impact on me, its the type of story that you keep thinking about hours, even days after you've seen it.
The anime however, is not as good as the manga but still a great watch. The Gaiden arc actually starts in Saiyuki episode 40 and 41. So you should watch those two episodes before watching these OVAs. Other than that it is not necessary to watch Saiyuki or any of the sequels before this, though I suggest you do because the whole series is great :) Saiyuki Burial is next in chronological order.